Stability of Volterra diffusion equations with time delays

摘要

This paper is concerned with asymptotic stability of a system of reaction-diffusion equations which is expressed in terms of Volterra integrals, under homogeneous Dirichlet boundary conditions. The effect of diffusion and delays on the stability of the system are analyzed, and sufficient conditions are given for the existence of positive solutions of the corresponding steady-state problem. Their global attraction with respect to nonnegative solutions of the time-dependent system is discussed. The main tools are Lyapunov functionals, positive definite kernels, and Laplace transforms.