Generalised Boussinesq model with variable coefficients

The global solvability of the boundary value problem for mass transfer equations has been proven, in which the coefficients of mass expansion and reaction nonlinearly depend on the concentration of the substance, and also depend on spatial variables. The mathematical apparatus is adapted to a specific boundary value problem to prove its solvability with minimal requirements for the initial data. Additional properties of the weak solution are established and their applications are discussed.