On boundary value problems for the Boussinesq-type equation with dynamic and non-dynamic boundary conditions

Year 2023, Volume: 7 Issue: 2, 377 - 386, 23.07.2023

Muvasharkhan Jenaliyev , Arnay Kassymbekova Madi Yergaliyev , Bekzat Orynbasar

https://doi.org/10.31197/atnaa.1215178

Abstract

The work studies boundary value problems with non-dynamic and dynamic boundary conditions for one- and two-dimensional Boussinesq-type equations in domains representing a trapezoid, triangle, "curvilinear" trapezoid, "curvilinear" triangle, truncated cone, cone, truncated "curvilinear" cone, and "curvilinear" cone. Combining the methods of the theory of monotone operators and a priori estimates, in Sobolev classes, we have established theorems on the unique weak solvability of the boundary value problems under study.

Keywords

Boussinesq equation, \; dynamical boundary condition, \; non-cylindrical domains, \; non-dynamical boundary condition

Supporting Institution

the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan

Project Number

AP09258892

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