Properties of the Solution of a Problem for a Pseudoparabolic Equation in a Non‐Cylindrical Domain

ABSTRACT In this paper, we investigate a boundary value problem for a third‐order pseudoparabolic equation posed in a non‐cylindrical domain. Unlike most existing studies that are restricted to rectangular domains, our analysis focuses on a non‐cylindrical domain with respect to the time variable, which requires the development of new techniques for treating nonlocal initial conditions. By applying the method of functional parametrization, we establish the existence and uniqueness of a solution and derive a series of a priori estimates for the solution as well as for its first‐ and mixed‐order derivatives.