Boundary value problem for nonlinear mass-transfer equations under Dirichlet condition

Global solvability of a boundary value problem for nonlinear mass-transfer equations under innhomogeneous Dirichlet condition for substance's concentration is proved. For a velocity vector we use a homogeneous Dirichlet condition. The model under consideration generalizes the Boussinesq approximation since the reaction coefficient depends nonlinearly on substance's concentration and depends on spatial variables. Sufficient conditions were established for initial data of boundary value problem under which its solution is unique and also there were determined the conditions under which the maximum principle for substance's concentration is valid.