Global stability of stationary solutions of reaction-diffusion systems

AbstractWe give a condition which implies that the trivial solution, U ≡ 0, of a class of reaction-diffusion systems with homogeneous Dirichlet boundary conditions, is a global attractor for all nonnegative solutions. In certain cases, this condition, which relates the diffusion matrix and the domain to a parameter which depends on the nonlinear term, significantly improves similar conditions which can be obtained from energy estimates. Applications are given to equations arising in mathematical ecology