Well-posedness for a class of nonlinear degenerate parabolic equations

TL;DR

This paper establishes the well-posedness of a class of nonlinear degenerate parabolic equations with Robin boundary conditions using advanced functional analysis tools.

Contribution

It introduces new well-posedness results for semilinear weakly degenerate reaction-diffusion systems employing Gagliardo-Nirenberg inequalities.

Findings

Proved existence and uniqueness of solutions

Developed embedding results for weighted Sobolev spaces

Applied interpolation inequalities to degenerate equations

Abstract

In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces.