Muvasharkhan JENALİYEV, Arnay KASSYMBEKOVA, Madi YERGALİYEV, Bekzat ORYNBASAR

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

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,

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