Evolution Inclusions with Hille–Yosida Operator

Abstract

This chapter deals with a parabolic differential inclusion of evolution type involving a nondensely defined closed linear operator satisfying the Hille–Yosida condition and source term of multivalued type in Banach space . The topological structure of the solution set is investigated in the cases that the semigroup is noncompact. It is shown that the solution set is nonempty, compact and an $R_\delta$-set . It is proved on compact intervals and then, using the inverse limit method , obtained on noncompact intervals. Secondly, the existing solvability and the existence of a compact global attractor for the m-semiflow generated by the system are studied by using measures of noncompactness . As samples of applications, we apply the abstract results to some classes of partial differential inclusions.