UNCG PDE Conference 2023

The PDE 2023 virtual three-day conference featured seven plenary lectures by world renowned experts.

• Thomas Bartsch, Professor and Chair of Analysis at the University of Giessen (Justus-Liebig-Universität Gießen)
• Alina Chertock, The LeRoy B. Martin, Jr. Distinguished Professor and Head of the Mathematics Department at NC State University 
• Manuel del Pino, Professor of Mathematics at the University of Bath
• Qiang Du, Fu Foundation Professor of Applied Mathematics at the Department of Applied Physics and Applied Mathematics (APAM), Fu Foundation School of Engineering and Applied Science (SEAS), Columbia University
• Irene Fonseca, Kavčić-Moura University Professor of Mathematics, Director of Center for Nonlinear Analysis, Carnegie Mellon University
• Peter Monk, Unidel Professor of Mathematical Science at the University of Delaware
• Chi-Wang Shu, Theodore B. Stowell University Professor of Applied Mathematics at Brown University

Thomas Bartsch, University of Giessen
Normalized solutions to nonlinear Schrödinger equations with potential
Abstract: The talk will be concerned with the existence of solutions of the non-linear Schrödinger equation –Δu + V(x)u + λu = f(u) on R^N or on domains Ω ⊂ R^N when the L^2-norm of the solution is prescribed. The problem of normalized solutions has received a lot of attention in recent years but still much less understood compared with the problem when the L^2 norms are free. We discuss this problem and present recent results. The talk is based on work with Riccardo Molle, Matteo Rizzi, Gianmaria Verzini, Shijie Qi and Wenming Zou.

Alina Chertock, North Carolina State University
Asymptotic preserving numerical methods for singularly perturbed problems
Abstract:
Solutions of many nonlinear PDE systems reveal a multiscale character; thus, their numerical resolution presents some major difficulties. Such problems are typically characterized by a small parameter representing, say, a low Mach or Fraude number. In the limiting regimes, the propagation speeds are very low, and therefore the use of explicit numerical methods would require very restrictive time and space discretization steps due to the CFL condition and restrictions on the smallness of numerical diffusion. This becomes rapidly too costly from a practical point of view, and consequently, numerical solutions for small parameter values may be out of reach. Moreover, standard implicit schemes, which will be uniformly stable, may be inconsistent with the limiting problem and may provide a wrong solution in the zero limits. Thus, designing robust numerical algorithms whose accuracy and efficiency are independent of the values of the small parameter is an important and challenging task. A widely used numerical approach applicable in all-speed regimes is based on asymptotic preserving (AP) numerical methods. AP methods guarantee that for a fixed mesh size and time step, the numerical scheme should automatically transform into a consistent and stable discretization of the limiting system.
In this talk, we will present several AP schemes for Navier–Stokes–Korteweg equation, rotational shallow water equations with Coriolis, and, if time permits, kinetic equations with singular limits.

Manuel Del Pino, University of Bath
Dynamics of concentrated vorticities in 2D and 3D Euler flows
Abstract: A classical problem that traces back to Helmholtz and Kirchhoff is the understanding of the dynamics of solutions to the Euler equations of an inviscid incompressible fluid when the vorticity of the solution is initially concentrated near isolated points in 2d or vortex lines in 3d. We discuss some recent results on these solutions’ existence and asymptotic behavior. We describe, with precise asymptotics, interacting vortices, and traveling helices, and extension of these results for the 2d generalized SQG. This is research in collaboration with J. Dávila, A. Fernández, M. Musso, and J. Wei.

Qiang Du, Columbia University
Nonlocal modeling, analysis and computation: some recent development
Abstract:Nonlocality has become increasingly prominent in nature, leading to the development of new mathematical theories to model and simulate its impact. In this lecture, we will concentrate on nonlocal models that involve interactions with a finite horizon, examining their significance in understanding phenomena involving potential anomalies, singularities, and other effects that arise from nonlocal interactions. Furthermore, we will present recent analytical studies that explore nonlocal operators and function spaces, discussing how they contribute to the development of robust numerical algorithms.

Irene Fonseca, Carnegie Mellon University
Phase separation in heterogeneous media
Abstract:
Modern technologies and biological systems, such as temperature-responsive polymers and lipid rafts, take advantage of engineered inclusions, or natural heterogeneities of the medium, to obtain novel composite materials with specific physical properties. To model such situations by using a variational approach based on the gradient theory, the potential and the wells may to depend on the spatial position, even in a discontinuous way, and different regimes should be considered. In the critical case case where the scale of the small heterogeneities is of the same order of the scale governing the phase transition and the wells are fixed, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. In the subcritical case with moving wells where the heterogeneities of the material are of a larger scale than that of the diffuse interface between different phases, it is observed that there is no macroscopic phase separation and that thermal fluctuations play a role in the formation of nanodomains. The supercritical case for fixed wells is also addressed, and a partial characterization of the limit energy is given.
This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands) and Likhit Ganedi (Aachen University, Germany), based on previous results also obtained with Adrian Hagerty (USA) and Cristina Popovici (USA).

Peter Monk, University of Delaware
Development of a coupled Trefftz and finite element method for approximating Maxwell’s equations
Abstract: The talk focuses on developing a discontinuous Galerkin method for the time harmonic Maxwell system. This method is based on the use of a finite element grid, but uses plane wave solutions of Maxwell’s equations on each element to approximate the global field. Because each basis function satisfies Maxwell’s equations, the problem can be reduced to a coupled linear system on the faces of the grid. Arbitrarily high order of convergence can be achieved by taking more planes waves in suitable directions element by element, although ill-conditioning must be carefully controlled. Unfortunately this method has severe deficiencies when applied to some problems involving screens and transmission lines. To remedy this, we have coupled polynomial finite element methods with the plane wave scheme. I shall report on the history of Trefftz-DG methods and the current state of this effort.

Chi-Wang Shu, Brown University
Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs
Abstract: In scientific and engineering computing, we encounter time-dependent partial differential equations (PDEs) frequently.  When designing high order schemes for solving these time-dependent PDEs, we often first develop semi-discrete schemes paying attention only to spatial discretizations and leaving time t continuous.  It is then important to have a high order time discretization to main the stability properties of the semi-discrete schemes.  In this talk we discuss several classes of high order time discretization, including the strong stability preserving (SSP) time discretization, which preserves strong stability from a stable spatial discretization with Euler forward, the implicit-explicit (IMEX) Runge-Kutta or multi-step time marching, which treats the more stiff term (e.g. diffusion term in a convection-diffusion equation) implicitly and the less stiff term (e.g. the convection term in such an equation) explicitly, for which strong stability can be proved under the condition that the time step is upper-bounded by a constant under suitable conditions, the explicit-implicit-null (EIN) time marching, which adds a linear highest derivative term to both sides of the PDE and then uses IMEX time marching, and is particularly suitable for high order PDEs with leading nonlinear terms, and the explicit Runge-Kutta methods, for which strong stability can be proved in many cases for semi-negative linear semi-discrete schemes.  Numerical examples will be given to demonstrate the performance of these schemes.

All times are Eastern Daylight Time (GMT -4:00).

6/9 Friday
09:45 am – 10:00 am: Welcome Remarks
10:00 am – 10:15 am: History and Music Videos
Yagerline – A Group of Trees Deep in Thought
Katie Pelikan – Good Night My Someone
10:15 am – 10:30 am: Conference Dedication to Pavel Drábek
10:30 am – 11:15 am: Special Presentation by Petr Girg
BREAK (15 min)
11:30 am – 12:30 pm: Plenary Lecture by Irene Fonseca “Phase Separation in Heterogeneous Media“
BREAK (30 min)
01:00 pm – 02:00 pm: (Optional) Technical Support for Screen Sharing
02:00 pm – 03:40 pm: Parallel Sessions
04:00 pm – 05:00 pm: Plenary Lecture by Alina Chertock “Asymptotic Preserving Numerical Methods for Singularly Perturbed Problems”

6/10 Saturday
10:00 am – 11:00 am: Plenary Lecture by Manuel Del Pino “Dynamics of concentrated vorticities in 2D and 3D Euler flows”
BREAK (10 min)
11:10 am – 12:10 pm: Parallel Sessions
BREAK (50 min)
01:00 pm – 02:00 pm: Plenary Lecture by Qiang Du “Nonlocal modeling, analysis and computation: some recent development”
BREAK (10 min)
02:10 pm – 03:10 pm: Parallel Sessions
BREAK (5 min)
03:15 pm – 04:00 pm: Meet and Greet with Pavel Drábek
04:00 pm – 05:00 pm: Plenary Lecture by Peter Monk “Development of a coupled Trefftz and finite element method for approximating Maxwell’s equations”

6/11 Sunday
10:00 am – 11:00 am: Plenary Lecture by Chi-Wang Shu “Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs”
BREAK (10 min)
11:10 am – 12:10 pm: Parallel Sessions
BREAK (50 min)
01:00 pm – 02:40 pm: Parallel Sessions
BREAK (20 min)
03:00 pm – 04:00 pm: Plenary Lecture by Thomas Bartsch “Normalized solutions to nonlinear Schrödinger equations with potential“
04:00 pm – 04:15 pm: Closing Remarks
04:15 pm – 05:00 pm: Chat with Pavel Drábek

Friday, June 9th
Today’s afternoon parallel sessions will take place from 2:00 to 3:40p.

Friday Afternoon Session 1 | Five Talks
Chair: Ananta Acharya
2:00 – 2:20p: Talbi, I. “Efficient Chaotic Generators for Image Encryption Algorithms”
2:20 – 2:40p: Rudzko, J. “Classical and Mild Solution of the Cauchy Problem for a Mildly Quasilinear Wave Equation with Discontinuous and Distributional Initial Conditions”
2:40 – 3:00p: Matsoukas, A. “The double phase Dirichlet problem when the lowest exponent equals to 1”
3:00 – 3:20p: Zhang, B. “Stability and Formulas for Lyapunov Functions for Systems of Partial Differential Equations”
3:20 – 3:40p:

Friday Afternoon Session 2 | Five Talks
Chair: Oscar Agudelo
2:00 – 2:20p: El Hajj, L. “Radial symmetry for an elliptic PDE with a free boundary”
2:20 – 2:40p: Nichols, D. “A uniqueness result for a p-Laplacian infinite semipositone problem involving nonlinear boundary conditions”
2:40 – 3:00p: Osorio, S. H. “Shooting method applied to a semipositone Φ-Laplacian problem”
3:00 – 3:20p: Agudelo, O. “Hamiltonian Elliptic systems with concave-convex nonlinearities, Part 1”
3:20 – 3:40p: Vélez, C. “Hamiltonian Elliptic systems with concave-convex nonlinearities, Parte II”

Friday Afternoon Session 3 | Five Talks
Chair: Satyajith Bommana Boyana
2:00 – 2:20p: Wang, G. “Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise”
2:20 – 2:40p: Chao, Z. “An effective finite element iterative solver for a Poisson-Nernst-Planck ion channel model”
2:40 – 3:00p: Xue, X. “Convergent Finite Difference Methods with Higher Order Local Truncation Errors for Stationary Hamilton-Jacobi Equations”
3:00 – 3:20p: Boyana, S.B. “Dual-Wind Discontinuous Galerkin Method and its Application to an Optimal Control Problem”
3:20 – 3:40p: Abderrahim, S. M. “A Numerical Analysis of Losbia Bortana’s Life Cycle with Real-Seasonal Temperature Data”

Friday Afternoon Session 4 | Five Talks
Chair: Senoussi Guesmia
2:00 – 2:20p: Mammar, I. “Prion disease models with pulsed effect”
2:20 – 2:40p: Dimou, H. “Alienation problem for the system of two functional equation”
2:40 – 3:00p: Ansari, H. “Existence, Uniqueness, Boundedness and Long-term Behavior of Solutions to an SIR Model with Intermittent Treatment”
3:00 – 3:20p: Zhang, Z. “Traveling wave solutions for a general epidemic model”
3:20 – 3:40p: Guesmia, S. “Elasticity system in noncylindrical domains with stretched cross-sections”

Friday Afternoon Session 5 | Five Talks
Chair: Lukas Kotrla
2:00 – 2:20p: Cengizci, S. “Simulating magnetohydrodynamic duct flows at high Hartmann numbers”
2:20 – 2:40p: Valdebenito, D.A. “Boundary layer problems involving anisotropic viscous coefficients”
2:40 – 3:00p: Kotrla, L. “Fluid flow through porous media over included bedrock”
3:00 – 3:20p: Wang, T. “Periodic solutions of incompressible Navier-Stokes flow in a 2D bounded domain”
3:20 – 3:40p: Wang, Z-Q. “Coupled nonlinear elliptic equations with mixed couplings”

Saturday, June 10th
Today’s six morning parallel sessions will take place from 11:10a to 12:10p.

Saturday Morning Session 1 | Three Talks
Chair: Yi Hu
11:10 – 11:30a: El Aïdi, M. “On an upper bound of the number of the negative eigenvalues of a generalized Schrödinger operator on a tree”
11:30 – 11:50a: Gupta, S. “Generalized Choquard Schrodinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces”
11:50 – 12:10p: Hu, Y. “Rotational Nonlinear Schrödinger Equation with Harmonic or Repulsive Potentials”

Saturday Morning Session 2 | Three Talks
Chair: Pamela Guerrero
11:10 – 11:30a: Onyido, M. A. “Asymptotic dynamics of a three-species hybrid competition”
11:30 – 11:50a: Yang, M. “Magic angles of twisted multilayer graphene”
11:50 – 12:10p: Guerrero, P. “Study of the modified BBM equation”

Saturday Morning Session 3 | Three Talks
Chair: Siham Boukarabila 
11:10 – 11:30a: Arora, R. “A large class of nonlocal elliptic equations wit singular nonlinearities”
11:30 – 11:50a: Han, Z. “Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications”
11:50 – 12:10p: Boukarabila, S. “Nonlocal KPZ-type system”

Saturday Morning Session 4 | Three Talks
Chair: Dhabaleswar Mohapatra
11:10 – 11:30a: Baghdad, S. “On partial fractional differential equations in Fréchet spaces”
11:30 – 11:50a: Tewfik, G.M. “A Struwe compactness result for a critical p-Laplacian equation involving critical and subcritical Hardy potential on compact Riemannian manifolds”
11:50 – 12:10p: Mohapatra, D. “Time fractional heat equation of (n + 1)-dimension with type-1 and type-2 fuzzy uncertainty”

Saturday Morning Session 5 | Three Talks
Chair: Gerard Awanou
11:10 – 11:30a: Awanou, G. “On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations”
11:30 – 11:50a: Faraci, F. “Some uniqueness results for strongly singular problems”
11:50 – 12:10p: Kumar, D. “Hölder regularity results for a class of nonlocal double phase problems”

Saturday Morning Session 6 | Three Talks
Chair: Ani Tumanyan
11:10 – 11:30a: Tumanyan, A. “Normal solvability and the Fredholm properties for a class of regular hypoelliptic operators”
11:30 – 11:50a: Baymout, L. “The Bifurcations of limit cycles from a class of non-linear differential system”
11:50 – 12:10p: 

Today’s afternoon parallel sessions will take place from 2:10p to 3:10p.

Saturday Afternoon Session 1 | Three Talks
Chair: Amlan Kanti Halder
2:10 – 2:30p: Halder, A. K. “Symmetries and Reductions of a Variable-Coeffcient Hirota-Satsuma Coupled Korteweg-de Vries System”
2:30 – 2:50p: Henderson, A. “On the effects of density-dependent dispersal on ecological models with logistic and weak Allee type growth terms”
2:50 – 3:10p: Soufiane, B. “Competition model between the same species in chemostat”

Saturday Afternoon Session 2 | Three Talks
Chair: Dustin Nichols
2:10 – 2:30p: Younes, A. “Regularizing effects on elliptic equations involving a superquadratic gradient term”
2:30 – 2:50p: Chaayra, T. “Gaussian estimation for discretely observed Brennan-Schwartz diffusion process based on martingales approach”
2:50 – 3:10p: Taarabti, S. “On a fourth-order Neumann problem in variable exponent spaces”

Saturday Afternoon Session 3 | Three Talks
Chair: Tina Mai
2:10 – 2:30p: Olunna, M. “Microscopy image segmentation using highly nonlinear PDE”
2:30 – 2:50p: Mai, T. “Multiscale simulations for dual-continuum Richard’s equations”
2:50 – 3:10p: Nguyen, P. “Numerical differentiation by the polynomial-exponential basis”

Saturday Afternoon Session 4 | Three Talks
Chair: Nirjan Biwas
2:10 – 2:30p: Cossio, J. “Shooting from singularity to singularity and a quasilinear p-Laplacian-Beltrami equation with indefinite weight”
2:30 – 2:50p: Fonseka, N. “Σ-shaped bifurcation curves for classes of reaction diffusion equations with non-linear boundary conditions”
2:50 – 3:10p: Biwas, N. “Fourth order semipositone problems on R^N”

Saturday Afternoon Session 5 | Two Talks
Chair: Eunkyung Ko
2:10 – 2:30p: Ko, E. “Multiplicity result of positive solutions for a Schrödinger-type singular elliptic equation”
2:30 – 2:50p: Harkat, S.” Asymptotic behavior of solutions of nonlinear parabolic equations defined on non-cylindrical domains becoming unbounded”
2:50 – 3:10p: Amira, B. A.  “Asymptotic behavior of positive solutions of a nonlinear elliptic problem involving the fractional p-Laplacian”

Sunday, June 11th
Today’s morning sessions parallel sessions will take place from 11:10a to 12:10p.

Sunday Morning Session 1 | Three Talks
Chair: Falko Baustian
11:10 – 11:30a: Soares, M. “Energy Estimates for Seminodal Solutions to na Elliptic System with Mixed Couplings”
11:30 – 11:50a: Atteya, M. J. “Notes of the Yang-Baster Equation”
11:50 – 12:10p: Baustian, F. “Fučík systems for Dirichlet and Neumann boundary conditions”

Sunday Morning Session 2 | Three Talks
Chair: Nalin Fonseka
11:10 – 11:30a: —
11:30 – 11:50a: Ardra, A. “On a shape derivative formula for the Robin p-Laplace eigenvalue problem with a potential”
11:50 – 12:10p: Somia, A. “The fractional regularity of the fractional heat equation and applications to deterministic generalized KPZ equation”

Sunday Morning Session 3 | Three Talks
Chair: Manki Cho
11:10 – 11:30a: Sagar, B. “An efficient mesh free numerical approach for solving fractional Gilson – Pickering equation arising in plasma physics”
11:30 – 11:50a: Ye, Q. “Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation”
11:50 – 12:10p: Cho, M. “Numerical Analysis of the electric potential of 2D electrostatic model via Steklov eigenproblems”

Sunday Morning Session 4 | Three Talks
Chair: Jochen Merker
11:10 – 11:30a: Pardo, R. “Uniform a-priori estimates for subcritical semilinear elliptic equations with a Carathéodory non-linearity”
11:30 – 11:50a: Sarkar, A. “On critically couples (s_1,s_2)-fractional system of Schödinger equations with Hardy potential”
11:50 – 12:10p: Merker, J. “How to obtain L^p-L^q estimates for elliptic and parabolic equations via logarithmic inequalities”

Sunday Morning Session 5 | Three Talks
Chair : Omar Boussaid
11:10 – 11:30a: Omar, B. “New criteria for quasi-convexity of quadratic forms in two dimensions”
11:30 – 11:50a: —
11:50 – 12:10p: Nastas, E. “On Semi-linear Evolution Equations & Cauchy Theorem”

Today’s afternoon sessions parallel sessions will take place from 1:00 to 2:40p.

Sunday Afternoon Session 1 | Five Talks
Chair: Bo Yang
1:00 – 1:20p: Ahrami, M. “Estimate bounds of the first eigenvalue of equations containing the p-Laplacian operator”
1:20 – 1:40p: El Allaoui, A. “Solvability of Langevin fractional differential equation of higher-Order with integral boundary conditions”
1:40 – 2:00p: Yang, B. “Radially symmetric positive solutions of the Dirichlet problem for p-Laplacian equation”
2:00 – 2:20p: Bobvok, V. “Improved Friedrichs inequality for a subhomogeneous embedding”
2:20 – 2:40p: Dieb, A. “Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods”

Sunday Afternoon Session 2 | Five Talks
Chair: Satyanarayana Engu
1:00 – 1:20p: Abney, R. “Nonradiating orbital motions”
1:20 – 1:40p: Ho, K. “The boundedness of solutions to elliptic problems involving double phase operator and critical growth”
1:40 – 2:00p: Engu, S. “On the solutions of a forced Burgers equation”
2:00 – 2:20p: Kumar, A. “Strict Monotonicity of the Torsional Rigidity over Annular Domains”
2:20 – 2:40p: Allaoui, Y. “Existence of Solutions of fractional Lane Eden equation with integral boundary condition”

Sunday Afternoon Session 3 | Five Talks
Chair: Byungjae Son
1:00 – 1:20p: Son, B. “Positive solutions to one-dimensional double phase problems”
1:20 – 1:40p: Acharya, A. “The diffusive Lotka-Volterra competition model in fragmented patches I: Coexistence”
1:40 – 2:00p: Jana, R. “Positive solutions for fractional p- Laplace semipositone problem with superlinear growth”
2:00 – 2:20p: Li, S. “On the Maxwell-Bloch System in the Sharp-Line Limit Without Solitons”
2:20 – 2:40p: Sengouga, A. “Explicit estimates for the energy of a traveling string damped at one end”

Sunday Afternoon Session 4 | Five Talks
Chair: Thu Thu Anh Le 
1:00 – 1:20p: Le, T. “A globally convergent numerical method for solving a coeffocient inverse problem for a hyperbolic equation with experimental data”
1:20 – 1:40p: Khoa, V. A. “An explicit Fourier-Klibanov method for an age-structured population diffusion Gompertz model”
1:40 – 2:00p: —
2:00 – 2:20p: Sahoo, A.K. “Physics Informed Neural Networks for Approximating the Solutions to Vibration Equation of Large Membranes”
2:20 – 2:40p: Le, T. T. A. “A sampling-type method combined with deep learning for inverse scattering with one incident wave”

Sunday Afternoon Session 5 | Five Talks
Chair: Jingchun Chen
1:00 – 1:20p: Baibeche, S. “On the stability of transmission problem for wave equations under effects of microtemperatures in the presence of Neutral delay”
1:20 – 1:40p: He, C. “Vlasov-Poisson-Fokker-Planck equation in modulation space”
1:40 – 2:00p: Chen, J. “Fundamental solution of fractional Kolmogorov-Fokker-Planck equation”
2:00 – 2:20p: Bag, M. “Optimal Boundary Control For The Cahn-Hilliard-Navier-Stokes Equations”
2:20 – 2:40p: Ghosh, M. “Isoperimetric inequalities for Zaremba problems”

The combined proceedings of the 2021/2023 UNC Greensboro PDE Conference Series were published by the Electronic Journal of Differential Equations:

• Mohammed Ahrami, Zakaria El Allali; Lower bounds on the fundamental spectral gap with Robin boundary conditions. 
• Gerard Awanou; Discrete Aleksandrov solutions of the Monge-Ampere equation.
• Falko Baustian, Vladimir Bobkov; Basisness of Fucik eigenfunctions for the Dirichlet Laplacian.
• Manki Cho, Mauricio A. Rivas; On the L^2-orthogonality of Steklov eigenfunctions.
• Xiaobing Feng, Thomas Lewis, Kellie Ward; A narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs.
• Daniel X. Guo; Semi-Lagrangian forward methods for some time-dependent nonlinear partial differential equations.
• Rohit Kumar, Abhishek Sarkar; Multiple solutions for a weighted p-Laplacian problem.
• Thomas Lewis, Aaron Rapp, Yi Zhang; Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs.
• Timothy Robertson; Wellposedness of Keller-Segel systems in mixed norm spaces.
• Dario A. Valdebenito; On solutions arising from radial spatial dynamics of some semilinear elliptic equations.
• Zhuoru Chen, Taige Wang, Xiangfei Xie; Bilinear estimates posed in finite domains in 2D and 3D.
• Petr Girg, Lukas Kotrla, Anezka Svandova; p-Laplacian in phenomenological modeling of flow in porous media and CFD simulations.
• Ani Tumanyan; Normal solvability and Fredholm properties for special classes of hypoelliptic operators.
• Zhenbu Zhang; Traveling wave solutions for an epidemic model.

Main Editors: Richard Fabiano and Yi Zhang

Associate Editors: Maya Chhetri, Tom Lewis and Ratnasingham Shivaji

2023 Conference Summary and Feedback

In the opening ceremony of the 2023 Conference, we played a UNCG History Video and broadcasted two musical performances, one by a UNCG School of Music student and another by one of our Mathematics Majors, and welcome remarks by Terri Shelton (Vice Chancellor for Research and Engagement). Sat Gupta (Head, Department of Mathematics and Statistics) also welcomed the participants. This conference was sponsored by the UNC Greensboro Office of Research, UNC Greensboro Department of Mathematics and Statistics, and Helen Barton Excellence Professorship Funds.

The 2023 conference was also dedicated to Professor Pavel Drabek (University of West Bohemia, Czech Republic) in celebration of his 70^th birthday and his outstanding contributions to differential equations. Professor Petr Girg (University of West Bohemia) made a special presentation on Pavel’s contributions.

The 2023 Conference featured 76 contributed talks and 7 plenary lectures by world renowned experts:

• Thomas Bartsch – University of Giessen
• Alina Chertock – NC State University
• Manuel del Pino – University of Bath
• Qiang Du – Columbia University
• Irene Fonseca – Carnegie Mellon University
• Peter Monk – University of Delaware and
• Chi-Wang Shu – Brown University.

Demographics:

• 240 registered participants
• Participants from 36 countries
• 56.7% either graduate students or recent PhDs (within three years)

Select Survey Feedback:

• Thank you for organizing this conference. It was a great opportunity to exchange knowledge, inspire innovation and foster collaborative connections. And very Happy Birthday 🎂to Professor Drabek☺️
• Thank you very much, UNC Greensboro PDE Conference
• Keep going
• The next copy of the conference, I hopeful it will remain virtual. Because it will offer the opportunity for several researchers from different continents of the world to attend it. I believe any conference satisfies this ideal i.e. it has diversity researchers will become better for all. In addition to that, the online style will help the participators to overcome some issues, like getting visas, breaking their teaching work for conference days and the cost of travailing the conference location.
• Thank you for organizing this wonderful conference.
• The conference was very organized and a great experience to bring together experts and young mathematicians from all over the world. The material presented was very interesting on various areas and topics related to PDEs. It was also very pleasant to learn some of Pavel Drabek’s scientific achievements, which were not well known by all of us. Lastly, I would like to comment that I just expected a bit more uniform distributed people in the talk rooms in the parallel session. There were time and space limitations so, this is just a comment or a remark!  I would like to thank warmly the organizers for letting me give a talk to this great conference. I am looking forward to seeing you in the next!
• I would like to congratulate you for this great event.
• I really enjoyed the conference.  I had learned a lot about some really interesting topics. Overall, it’s been a great experience.
• And I was impressed with the quality of the conference organization. It is clear that a lot of effort has gone into planning and executing the event. Wish you all the best, I’m looking forward to seeing you in the next conference 2025.
• Thank you to the organizers for hosting such an excellent scientific event with a diverse and engaging program that catered to a wide range of research interests in PDE. The virtual format of the conference worked seamlessly, allowing for international participation and providing a user-friendly platform for presentations and discussions. Overall, the conference was a rewarding and enriching experience.

Sponsored by the UNC Greensboro Office of Research and Engagement, the UNC Greensboro Department of Mathematics and Statistics, and Helen Barton Excellence Professorship Funds

Organizers:

Program Chair: Yi Zhang

Organizing Committee: Maya Chhetri, Rich Fabiano, Tom Lewis (Chair), Yi Zhang, and Ratnasingham Shivaji

Website Organizer: C. Matthew Farmer

Contact: Ratnasingham Shivaji – shivaji@uncg.edu