Non Linear Hyperbolic-Parabolic Systems with Dirichlet Boundary Conditions

TL;DR

This paper establishes the well-posedness and stability of a class of nonlinear, nonlocal hyperbolic-parabolic systems with Dirichlet boundary conditions, relevant to population dynamics and epidemiology models.

Contribution

It proves well-posedness and stability estimates for a new class of nonlinear, nonlocal hyperbolic-parabolic systems with Dirichlet boundary conditions.

Findings

Proved well-posedness of the systems

Derived stability estimates on solutions

Applicable to models in population dynamics and epidemiology

Abstract

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on data and parameters are also provided. These equations appear in models devoted to population dynamics or to epidemiology, for instance.