On Nonlinear Parabolic Equation in Nondivergent Form with Implicit Degeneration and Embedding Theorems

TL;DR

This paper investigates the solvability and behavior of solutions for a class of implicit degenerating nonlinear parabolic equations, and explores related function spaces, embedding, and compactness theorems.

Contribution

It introduces new results on the solvability and properties of solutions for implicit degenerating nonlinear parabolic equations, along with embedding theorems for associated function spaces.

Findings

Proved solvability conditions for the implicit degenerating nonlinear parabolic equation

Established embedding and compactness theorems for related function spaces

Analyzed the behavior of solutions in various function space settings

Abstract

The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with Sobolev spaces are investigated, embedding and compactness theorems for these spaces are proved