- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 2
- On boundary value problems for the Boussinesq-type equation with dynamic and non-dynamic boundary co...
On boundary value problems for the Boussinesq-type equation with dynamic and non-dynamic boundary conditions
Authors : Muvasharkhan Jenaliyev, Arnay Kassymbekova, Madi Yergaliyev, Bekzat Orynbasar
Pages : 377-386
Doi:10.31197/atnaa.1215178
View : 49 | Download : 92
Publication Date : 2023-07-23
Article Type : Research Article
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