Research

I’m interested in partial differential equations motivated by models in biology and traffic flow. I study theoretical tools to understand qualitative properties of hyperbolic systems of conservation laws in one dimension. I specifically try to look for conditions under which certain systems of conservation laws possess solutions through weak convergence methods.

Recently, I have been working in 2x2 systems of conservation laws describing repulsive and attractive chemotaxis which, roughly speaking, describe the motion of bacteria that are repelled or attracted by the gradients of chemical concentrations.

I have also studied continuum models of traffic flow with relaxation terms. I employ compensated compactness techniques to study the existence of weak global solutions for these kind of problems.

Publications

• Beltrán, J. D., Li, T. Critical threshold phenomena in a mixed-type system of conservation laws modeling attractive chemotaxis. J. Math. Phys., 66 (4), 2025.

• Beltrán, J. D., Li, T. “Zero relaxation limit for a non-strictly hyperbolic system arising in traffic flow with dominant diffusion”. Accepted for publication on “Analysis and PDE in Latin America, ICMAM 2023-2024” Conference Proceedings. Birkhäuser Cham. 2025.

Master thesis

Global Lipschitz Continuous Solutions for a Linearly Damped p-system. Beltrán, J. D.,Rendón, L. Universidad Nacional de Colombia, Bogotá.

Seminars

I currently participate in the PDE Seminar at The University of Iowa headed by Professor Tong Li. We usually have weekly meetings on Wednesdays 15:30 -16:20 (Central Time).

Seminars (past).

This semester (March - July 2021) we are running a student seminar called “Conservation Laws and Partial Differential Equations” (in Spanish) headed by Professor Leonardo Rendón from the National University of Colombia. Here you can find a brief description (in Spanish) of the topics we will be covering this semester.