Differential inequalities for systems of degenerate parabolic operators

Abstract

The Prodi-Westphal theorem is generalized to systems of differential inequalities for nonlin ear nonuniformly parabolic operators of the form [d] The function F[d] is defined for (x,t) in a hypercylinder [d] where G is a bounded open domain in R^m. Suppose that F[d] is elliptic with respect to [d] and that [d] Since it is admissible that [d] at some points of [d] may be nonuniformly parabolic. Two additional theorems on differential inequalities for systems are proved and the results are applied to the paroblem of investigating stability of solutions of certain systems of degenerate parabolic equations,[d]