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 entropy global weak solutions for these kind of problems.

Here you can find my research statement.

Publications

• Beltrán, J. D., Li, T. Global existence and zero relaxation limit for a hyperbolic system arising in traffic flow with large data. J. Differ. Equ. 467, 114344, (2026).

• Beltrán, J. D., Li, T. Zero relaxation limit for a non-strictly hyperbolic system arising in traffic flow with dominant diffusion. Cardona Sanchez, D., Grajales, B. (eds). Analysis and PDE in Latin America, ICMAM 2024,Trends in Mathematics. Birkhäuser Cham. 2026.

• Beltrán, J. D., Li, T. Critical threshold phenomena in a mixed-type system of conservation laws modeling attractive chemotaxis. J. Math. Phys., 66, 041510, (2025).

Preprints

• Beltrán, J. D., Li, T. Global existence for a non-strictly hyperbolic system modeling blood flow in the half-line with large data. Submitted (2026).

Master’s thesis

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