Decay results in a cross-diffusion problem

Abstract

In this thesis, we investigate decay bounds in temporal and space for a cross-diffusion problem with the homogeneous Dirichlet, Neumann, and Robin boundary conditions we study temporal bounds under appropriate restrictions on the coefficients of the cross-diffusion problem. We show that solutions decay in L-2 at least as fast as e^-kt(k is a computable constant). In the spatial decay bound case, with homogeneous Dirichlet conditions prescribed on the lateral surface of the cylinder, it is shown that for fixed time and under certain restrictions on the coefficients, solutions decay in L-2 at least as fast e^-kz(k is a computable constants).