On the Smoothness of a Generalized Solution of the First Initial Boundary-Value Problem for Strongly Parabolic Systems in a Cylinder with Nonsmooth Base with Respect to Time Variable

Abstract

We consider the first initial boundary-value problem for strongly parabolic systems in an infinite cylinder with nonsmooth boundary. We establish conditions for the existence of generalized solutions, an estimate for this solutions, and an estimate for the derivative of the solution.