Existence and stability of summable generalized solutions in a mathematical model of a catalytic process in a boiling layer

For a system of first order partial differential equations describing a catalytic process in a boiling layer, we consider a mixed problem in the half-strip $ 0\le x\le h$, $t\ge0$. We prove the existence and uniqueness of a bounded summable generalized solution and study its stability. We prove the stabilization as $t\to\infty$ of the values of some physically meaningful functionals of solutions.