A problem for one class of pseudodifferential evolutionary equations multipoint in the time variable

Abstract

We establish the correct solvability of the multipoint (in the time variable) problem for the evolution equation with operator of differentiation of infinite order in generalized $S$-type spaces. The properties of the fundamental solution of this problem and the behavior of the solution $u(t, x)$ as $t \rightarrow +\infty$ are investigated.