People

Ratnasingham Shivaji

Ratnasingham Shivaji

Professor
H. Barton Excellence Professor
Department Head

Office: Petty 118
Phone: 334-5836
Email: r_shivaj@uncg.edu
Personal Website: http://www.uncg.edu/~r_shivaj/
Starting year at UNCG: 2011
Office Hours: TR 2:00 p.m. - 3:30 p.m.

Education

Degree(s): Ph.D. in Mathematics, Heriot-Watt University (1981)

Teaching

Spring 2019
  • MAT-390 LEC (Ordinary Differential Equatns), TR 11:00-12:15, PETT 7
  • MAT-709 IND (Topics in Computational Math), MW 3:30-4:45, PETT 150
  • MAT-790 IND (Directed Doctoral Research)
  • MAT-790 IND (Directed Doctoral Research)

Research

Member of the Research Group(s): Applied Math, Mathematical Biology
Current Students: Amila Muthunayake (Ph.D.), Nalin Fonseka (Ph.D.), Ananta Acharya (Ph.D.), Mohan Mallick
Former Students: Dagny Butler , Keri Spetzer (M.A.), Byungjae Son (Ph.D.), Quinn Morris (Ph.D.)

Research Interests: Study of nonnegative solutions to partial differential equations, arising in the modeling of natural phenomena that is dominated by reaction and diffusion. Recent results focus on singular problems, problems with nonlinear diffusion and effects of nonlinear boundary conditions.

Selected Publications

  • Positive solutions for a class of non-cooperative pq-Laplacian systems with singularities, K.D. Chu, D.D. Hai, R. Shivaji, Applied Math Letters (accepted for publication 2018).
  • A diffusive logistic equation with U-shaped density dependent dispersal on the boundary, J. Goddard, Q. Morris, C. Payne, and R. Shivaji, Topological Methods in Nonlinear Analysis (accepted for publication 2018).
  • Uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains, K. D. Chu, D. D. Hai, R. Shivaji, J. Math Anal. Appl. (accepted for publication 2018).
  • Analysis of positive radial solutions for a class of semipositone p-Laplacian problems with nonlinear boundary conditions, E. Lee, R. Shivaji, I. Sim, and B. Son, Commun. Pure Appl. Anal. (accepted for publicatin 2018).
  • Existence and multiplicity of positive radial solutions for singular superlinear elliptic systems in the exterior of a ball, D. D. Hai and R. Shivaji, J. Differential Equations (accepted for publications 2018).

Brief Biography

Ratnasingham Shivaji joined the University of North Carolina at Greensboro (UNCG) as Head in July 2011. Since January 2012, he is also serving as H. Barton Excellence Professor. Prior to joining UNCG, he served for twenty-six years at Mississippi State University (MSU), where he was honored as a W.L. Giles Distinguished Professor. He received his Ph.D in Mathematics from Heriot-Watt University in Edinburgh, Scotland in 1981 and his B.S (first class honors) from the University of Sri Lanka in 1977. He is a Fellow of the American Mathematical Society. Shivaji’s area of specialization is partial differential equations, and in particular, nonlinear elliptic boundary value problems. His research work has applications in combustion theory, chemical reactor theory, and population dynamics, and has been funded by the National Science Foundation and the Simon’s Foundation. Currently, he is serving as the PI on an NSF Math Ecology grant. To date, he has authored one hundred fifty research papers. He is a member of the Editorial Board of several mathematics journals. To date, he has directed one postdoctoral student, seventeen Ph.D. students (13 graduates, 4 current), fifteen M.S. graduates, and twenty-seven undergraduate research students.