INVESTIGATING WEAK SOLUTIONS FOR A SINGULAR AND DEGENERATE SEMILINEAR PARABOLIC EQUATION WITH A NONLINEAR INTEGRAL CONDITION

This article aims to study the existence and uniqueness of a weak solution for a singular and degenerate nonlinear parabolic equation with a generalized nonlinear integral condition of the second type. The proof of the existence and uniqueness of the weak solution to such a problem will be proceeded with in three steps. In the same regard, the solvability of the linear case of the problem at hand will be handled with the use of the Faedo-Galerkin method, a priori estimate, and by imposing some nonlinear conditions of the second kind.