Existence and Uniqueness of Solutions to a Class of Strongly Degenerate Equations

This paper deals with the existence and uniqueness of solutions to a class of doubly strongly degenerate equations.Owing to the degeneracies in the equation,the classical solutions of the problem may not exist.We firstly gave the definition of the weak solution of the problem considered,then by virtue of the regularized problem combined with the compensatory compact theorem,we proved the existence of the weak solution,finally,we showed the uniqueness of the weak solution by using Holmgren's method.