Attractivity For Cauchy Problem Of Reaction-diffusion Equations With Time Delays

This paper is concerned with attractivity of the solutions for theCauchy problem of two kinds of reaction-diffusion equations with time delays.Firstly, using the properties of nonnegative matrices and some differentialinequalities, some new suffcient conditions for the existence of invariant sets andglobal attractivity for the Cauchy problem of a class of reaction-diffusion equa-tions with time delays are obtained.Secondly, we consider the Cauchy problem on a kind of nonlinear impulsivereaction-diffusion equations. Using the fundamental solutions of parabolic partialdifferential equations, the existence of mild solutions are established. Applyingthe spectral properties of nonnegative matrices and establishing an integral in-equality with impulsive initial conditions, some results about the attractivity ofthis system are obtained.