On nonlinear parabolic equations with boundary conditions of the Bitsadze-Samarskii type

A non-local parabolic problem with a p-Laplacian and non-local boundary conditions of the Bitsadze-Samarskii type is considered. The existence of a solution is proved and estimates for such solutions are obtained. To study the non-local problem, a differential-difference equation of parabolic type is constructed, and the existence of a solution to such an equation is proved. The theory of maximal monotone and pseudomonotone operators is used in the proof. We also consider the conditions under which the composition of the p-Laplacian and the difference operator is a pseudomonotone operator. Note that, generally speaking, this composition is not a monotone operator.