The initial boundary problem is formulated for the model of catalytic bimolecular reactions limited by the lateral interactions of reactants and the surface diffusion of reactants to the reaction centers. The model of catalytic bimolecular reactions is based on the generalized kinetic BET model (GK BET model). It is shown that the problem is solved within the class of infinitely differentiable functions. The obtained results are the basis for finding the precise solutions and the numerical simulation.