Time-Variable Extension of the Solution of a Nonlocal Multipoint Problem for Partial Differential Equations with Constant Coefficients

Abstract

A problem with nonlocal multipoint conditions for the nth-order partial differential equation with constant coefficients is considered. In the case where conditions of strict averaging of time intervals are specified, the existence of a solution of the problem in a cylinder that is the Cartesian product of a time interval and a p-dimensional spatial torus is discussed. It is found that under certain conditions of separability of the roots of the characteristic equation for almost all (in the sense of the Lebesgue measure) coefficients of the equation and parameters of the conditions, the solution of the problem cannot be extended in the time variable beyond the extreme points at which the conditions are given.