Behavior of solutions to an inverse problem for a quasilinear parabolic equation

摘要

In this article we consider the inverse problem with anintegral condition by redefinition for a parabolic type equation. Theexistence of a weak solution of the inverse problem is proved by theGalerkin method.In a bounded domain with a homogeneous Dirichletcondition, sufficient conditions for the destruction of its solution in afinite time are obtained, and also the stability of the solution for theinverse problem with the opposite sign on the nonlinearity of the powertype.