Analysis of Inhomogeneous Boundary Value Problems for Generalized Boussinesq Model of Mass Transfer

The global solvability of the boundary value problem for the nonlinear mass transfer equations is proved under inhomogeneous Dirichlet boundary conditions for the velocity given on the entire boundary, and for the substance’s concentration, given on the part of the boundary. It is assumed that the reaction coefficient in one of the equations of the model depends nonlinearly on the substance’s concentration, and also depends on spatial variables. The local uniqueness of a weak solution of the boundary value problem is proved, the principle of maximum and minimum for the substance’s concentration is established. Several types of conditions for the reaction coefficient are considered, each of them has its own mathematical apparatus.