Direct and inverse problems for a singular system with slow and fast variables in chemical kinetics

Direct and inverse problems for singular systems with small parameter are stated, which describe catalytic reactions in chemical kinetics. The solution of the direct problem is based on the method of integral manifolds. The inverse problem reduces to finding the coefficients of the polynomial in the right-hand part of the slow equation according to the solution given on the slow surface of the system. The above arguments make it possible to obtain existence and uniqueness conditions for the coefficients in the right-hand part of the slow subsystem of the degenerate system.