On a class of evolution problems

Abstract

SynopsisA class of evolution problems is investigated [see (1.5), (1.6), (1.7) of the present paper] which includes, as a particular case, an evolution problem previously considered by a different author. Existence and uniqueness theorems are given in several function spaces. It is shown that, when the solution is required to belong to spaces of smooth functions, the problem becomes overdetermined. The necessary and sufficient integro-differential equations, to be satisfied by the datum, for the existence of a smooth solution, are given.