On the problem without initial conditions for a nonlinear degenerating parabolic system

Abstract

We indicate the classes for which a solution of the problem for a certain nonlinear degenerating parabolic system without initial conditions exists and is unique. The uniqueness conditions are established both in the case where restrictions are imposed on the behavior of solutions as $t \rightarrow -\infty$ and in the case where they are not imposed. The existence is proved for the arbitrary behavior of the right-hand side of the system as $t \rightarrow -\infty$.