Existence, uniqueness and large-time behaviour of (bounded) weak solutions to some classes of diffusive PDEs.
Many applications in physics, chemistry and biology can be modeled by reaction-(cross) diffusion systems, which describe the evolution of the densities or concentrations of a multicomponent system. The focus of the first part of the lecture will be on the mathematical properties of reversible reaction-diffusion systems based on entropy methods. Our goal will be to show how the entropy estimate can be used systematically to get bounds leading to the existence of strong or weak solutions, as well as bounds for the convergence rate to equilibrium.
The second part of this lecture will then be devoted to the study of the existence theory for cross-diffusion systems used in applications, for instance a population dynamics model describing the segregation of species due to competition or the Maxwell-Stefan equations modeling the evolution of a gaseous mixture.
Not necessary