Alekseev, G.; Soboleva, O. Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer. Mathematics2024, 12, 391.
Alekseev, G.; Soboleva, O. Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer. Mathematics 2024, 12, 391.
Alekseev, G.; Soboleva, O. Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer. Mathematics2024, 12, 391.
Alekseev, G.; Soboleva, O. Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer. Mathematics 2024, 12, 391.
Abstract
We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop mathematical apparatus of studying inhomogeneous boundary value problems under consideration. It is based on using of a weak solution of the boundary value problem and construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce original problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions.
Keywords
generalized Boussinesq model of mass transfer; binary fluid; inhomogeneous boundary conditions; global solvability; maximum principle; local uniqueness
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
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