Existence, uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities

摘要

This paper is devoted to the study of the initial value problem for parabolic systems with discontinuous nonlinearities from the viewpoint of the existence, uniqueness and stability of weak solutions. Also the relationship with the solutions of the corresponding differential inclusions is studied. Keywords Parabolic systems - Discontinuous nonlinearities - Initial value problems - Existence - Uniqueness - Stability Mathematics Subject Classification (2000) 35K45 Communicated by J. Hofbauer.