Solvability of a model for monomer-monomer surface reactions

A mathematical model for a monomer-monomer surface reaction is considered taking into account the surface diffusion of adsorbed particles of both reactants. The model is described by a coupled system of parabolic equations where some of them are defined in a domain and the other ones have to be solved on the domain surface. The existence and uniqueness theorem of a classic solution for the time-dependent problem is proved. Non-uniqueness of solutions for the steady-state problem is established.