Properties of the Solution of a Problem for a Pseudoparabolic Equation in a Non-Cylindrical Domain
Ospanov M. Merzetkhan A.
2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026
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.
boundary value problem , non-cylindrical domain , parameterization method , pseudoparabolic equation
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Faculty of Mathematics and Mechanics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
School of Artificial Intelligence and Data Science, Astana IT University, Astana, Kazakhstan
Faculty of Mathematics and Mechanics
School of Artificial Intelligence and Data Science
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026