On a Nonstationary Model of a Catalytic Process in a Fluidized Bed

In the half-strip 0 ≤ x ≤ h, t ≤ 0 we consider a mixed problem for an almost linear system of three first order PDEs, one of which does not involve derivatives with respect to t. We prove the existence and uniqueness of a generalized Holder continuous solution and generalized piecewise smooth and smooth solutions. For the piecewise smooth solution we prove the stabilization of some functionals as t → ∞.