# Fonseka, Dr. Nalin

### About

Dr. Nalin Fonseka joined Carolina University as an assistant professor of mathematics in the School of Arts and Sciences in Fall 2020. After receiving his bachelor’s degree from the University of Peradeniya, Sri Lanka in 2009, he has served as a lecturer at University of Peradeniya from 2010 to 2014. He earned his master’s degree in pure mathematics from Eastern Illinois University in 2015. He received his PhD in computational mathematics from the University of North Carolina at Greensboro in 2020 where he served as a teaching assistant for five years. He has taught various undergraduate mathematics classes since 2010 including hybrid and online classes. His research focuses on Differential Equations (Nonlinear Elliptic Boundary Value Problems) and Mathematical Ecology (Steady State Reaction-Diffusion Equations modeling population dynamics, including the density-dependent dispersal on the boundary and effects of exterior matrix hostility). His research work has resulted in articles published in several journals including the Advances in Nonlinear Analysis, Journal of Mathematical Analysis and Applications, Discrete and Continuous Dynamical Systems, Series S, and Mathematical Biosciences and Engineering. To date, Dr. Nalin Fonseka has collaborated with over 8 researchers including a renowned ecologist.

### Publications

**N. Fonseka**, J. Goddard II, Q. Morris, R. Shivaji, and B. Son, *On the effects of the exterior matrix hostility and a U-shaped density-dependent dispersal on a diffusive logistic growth model*, Discrete Contin. Dyn. Syst. Ser. S, (2018), 1-15.

**N. Fonseka**, R. Shivaji, B. Son, and K. Spetzer, *Classes of reaction-diffusion equations where a parameter influences the equation as well as the boundary condition*, J. Math. Anal. Appl., 476 (2019), no. 2, 480-494.

J. T. Cronin, **N. Fonseka**, J. Goddard II, J.Leonard, and R. Shivaji, *Modeling the effects of density-dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence*, Mathematical Biosciences, and Engineering. (2019), 17(2) : 1718-1742.

**N. Fonseka**, J. Machado, and R. Shivaji, *A study of logistic growth models influenced by the exterior matrix hostility and grazing in an interior patch*, Electron J. Qual. Theory Differ. Equ. (2020), No. 17, 1-11.

**N. Fonseka**, A. Muthunayake, R. Shivaji, and B. Son, *Singular reaction-diffusion equations where a parameter influences the reaction term and the boundary condition*, Topological Methods in Nonlinear Analysis, Vol 57, No 1 (2021), 221-242.

**N.** **Fonseka**, J. Goddard II, R. Shivaji, and B. Son, *A diffusive weak Allee effect model with U-shaped emigration and matrix hostility*, Discrete Contin. Dyn. Syst. Ser. B, 2020, 22 (11), No. 1531-3492.

A. Acharya, **N. Fonseka**, and R. Shivaji, *Analysis of reaction-diffusion systems where a parameter influences both the reaction terms as well as the boundary*, Boundary Value Problems, 2021 (1), 1-8.

A. Acharya, **N. Fonseka**, J. Quiroa, and R. Shivaji, *Sigma-shaped bifurcation curves*, Advances in Nonlinear Analysis, Volume 10 (2021), https://doi.org/10.1515/anona-2020-0180

A. Acharya, **N. Fonseka**, and R. Shivaji, *Sigma-shaped bifurcation curves for classes of elliptic systems*, Discrete Contin. Dyn. Syst. Ser. S., 2022, doi: 10.3934/dcdss.2022067.

### Manuscripts Submitted

**N. Fonseka**, J. Goddard, D. Nichols, K. Henderson, and R. Shivaji, *Modeling effects of matrix heterogeneity on population persistence at the patch-level*, (Submitted 2022).

A. Acharya, **N. Fonseka**, K. Henderson, and R. Shivaji, *Sigma-shaped bifurcation curves for classes of reaction diffusion equations with non-linear boundary conditions*, (Submitted 2022).

### Manuscripts in Preparation

A. Acharya, **N. Fonseka**, J. Goddard II, R. Shivaji, and B. Son, {\it On the effects of the exterior matrix hostility and a hump-shaped density dependent dispersal on a diffusive logistic growth model.}

A. Acharya, **N. Fonseka**, J. Goddard, K. Henderson, and R. Shivaji, On the effects of density-dependent dispersal on ecological models with logistic and Allee effect type growth terms.

**N. Fonseka**, A $2n+1$ solution theorem for classes of reaction diffusion equations.

**N. Fonseka**, A $2n$ solution theorem for classes of reaction diffusion systems with linear boundary conditions.

### Invited/Contributed Talks

**The 38th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE)**, University of North Georgia, Gainesville, GA, *Classes of reaction-diffusion equations where a parameter influences the equation as well as the boundary condition*, October 2018.

**The 14th Annual UNCG Regional Mathematics and Statistics Conference,** UNCG, Greensboro, NC, *Analysis of positive solutions for a logistic growth model with grazing*, November 2018.

**American Mathematical Society (AMS) Spring Southeastern Sectional Meeting**, Auburn University, Auburn, AL, *Classes of reaction-diffusion equations where a parameter influences the equation as well as the boundary condition*, March 2019.

**The 39th SEARCDE**, Embry-Riddle Aeronautical University, Daytona Beach, FL, *Singular reaction-diffusion equations where a parameter influences the reaction term and the boundary condition*, October 2019.

**The 15th Annual UNCG Regional Mathematics and Statistics Conference**, UNCG, Greensboro, NC, *On the effects of the exterior matrix hostility and a U-shaped density-dependent dispersal on a diffusive logistic growth model*, November 2019.

**AMS Fall Southeastern Sectional Meeting**, University of Florida, Gainesville, FL,

**AMS Annual Meeting**, Colorado Convention Center, Denver, CO,

**AMS Fall Southeastern Sectional Meeting** (virtual meeting), formerly at the University of Tennessee at Chattanooga, *A diffusive weak Allee effect model with U-shaped emigration and matrix hostility*, October 2020.

**AMS Fall Western Sectional Meeting** (virtual meeting), formerly at the University of Utah, *Analysis of reaction-diffusion systems where a parameter influences both the reaction terms as well as the boundary*, October 2020.

**AMS Annual Meeting** (virtual meeting), *A diffusive weak Allee effect model with U-shaped emigration and matrix hostility*, January 2021.

**AMS Spring Eastern Sectional Meeting** (virtual meeting), formerly at Brown University, *Sigma - shaped bifurcation curves*, March 2021.

**9th International Online Conference on "Mathematical Analysis, Differential Equation & Applications (MADEA 9)", ***Elliptic boundary value problems where a parameter affects both the equation and the boundary conditions*, June 2021.

**UNC Greensboro PDE Conference of 2021**, UNCG, Greensboro, NC, *Logistic growth model with U-shaped density-dependent dispersal and matrix hostility*, July 2021.

**10th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA)**, *Modeling the effects of density-dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence, August 2021.*

**10th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA)***, A multiplicity result for a class of reaction-diffusion equations, August 2021.*

**AMS Fall Central Virtual Sectional Meeting**, *A study of logistic growth models influenced by the exterior matrix hostility and grazing in an interior patch*, October 2021.

**5th International Conference on Mathematics (ICOM 2021)***, Modeling the effects of density-dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence, December 2021.*

**III International Conference on Mathematics and its Applications in Science and Engineering** **(ICMASE 2022)**, *Existence and multiplicity of positive steady states for classes of reaction diffusion equations*, July 2022.

### Poster Presentations

**SIAM (Society for Industrial and Applied Mathematics) Conference on Analysis of Partial Differential Equations (PD22), ***Boundary value problems where a parameter influences both the equation and the boundary conditions,* March 2022.

### Chairing Conference Sessions

III International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2022).

2nd International Conference on Mathematics and Mathematics Education (ICMME 2021).

### Fellowships

Project NExT Fellowship, MAA 2022 - 2023, Red'22 Cohort.

### Courses Taught

- Mathematics I
- Mathematics II
- Introduction to Statistics
- Math Lab
- Basic Mathematics
- College Algebra
- Precalculus I, II
- Calculus I, II
- Calculus w/ Business Applications
- Contemporary Topics in Mathematics