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

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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