On decay of entropy solutions to degenerate nonlinear parabolic equations with perturbed periodic initial data

TL;DR

This paper proves that entropy solutions to certain degenerate nonlinear parabolic equations decay over time when starting from initial data composed of a periodic function plus a vanishing function, under specific nonlinearity-diffusivity conditions.

Contribution

It establishes decay results for entropy solutions with perturbed periodic initial data under a precise nonlinearity-diffusivity assumption, extending understanding of long-term behavior.

Findings

Entropy solutions decay over time under given conditions

Decay holds for initial data combining periodic and vanishing functions

Results depend on specific nonlinearity-diffusivity assumptions

Abstract

Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the sense of measure).