Conditional Correctness of the Internal Boundary Value Problem of the Pseudoparabolic Equation with a Changing Time Direction

Abstract

We consider data and boundary conditions and data within the regularity domain of a pseudoparabolic equation with varying time direction. This problem cannot be solved in the sense of J. Hadamard. Based on A. N. Tikhonov's approach, this problem is investigated for conditional correctness, the uniqueness theorem is proved, and the evaluation of conditional stability on the set of correctness is established. This study uses methods of functional analysis and methods of the theory of functions of a complex variable.