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

Jenaliyev M. Kassymbekova A. Yergaliyev M. Orynbassar B.
2023 DergiPark

Advances in the Theory of Nonlinear Analysis and its Applications
2023 #7 Issue 2 377 - 386 pp.

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.

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

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Department of Dierential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Department of Dierential Equations

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