Global-in-time behavior of weak solutions to reaction–diffusion systems with inhomogeneous Dirichlet boundary condition

Abstract

We study reaction diffusion systems describing, in particular, the evolution of concentrations in general reversible chemical reactions. We concentrate on inhomogeneous Dirichlet boundary conditions. We first prove global existence of (very) weak solutions. Then, we prove that these – although rather weak – solutions converge exponentially in L1 norm toward the homogeneous equilibrium. These results are proven by means of L2-duality arguments and through estimates provided by the nonincreasing entropy.