PARABOLIC AND HYPERBOLIC SYSTEMS DETERMINED BY COERCIVE OPERATOR VALUED MEASURES

Abstract

In this paper we consider a class of distributed parameter systems governed by parabolic and hyperbolic partial differential equations containing operators which are measures. We prove existence, uniqueness and regularity properties of weak solutions. This covers the important and well established class of systems considered by J.L Lions as spe- cial case. Control problems with quadratic cost are treated for parabolic problems only. Following similar technique these results can be extended to hyperbolic systems also.