- Advances in the Theory of Nonlinear Analysis and its Application
- Volume: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 JENALİYEV, Arnay KASSYMBEKOVA, Madi YERGALİYEV, Bekzat ORYNBASAR
Pages : 377-386
Doi:10.31197/atnaa.1215178
View : 61 | Download : 98
Publication Date : 2023-07-23
Article Type : Research Paper
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