Approximation results for semigroups generated by multivalued linear operators and applications

Abstract

We establish convergence results for sequences of multivalued linear operators $A_n$. When each $A_n$ generates a differentiable semigroup, we state conditions for convergence of the corresponding semigroups and of the solutions of linear differential inclusions governed by $A_n$. Through a method already considered in the literature, this enables us to prove new convergence properties for a sequence of degenerate evolution equations. Applications to partial differential problems are also given.