p-Laplacian wave equations in non-cylindrical domains

TL;DR

This paper investigates the stability of p-Laplacian wave equations with strong damping in non-cylindrical domains, establishing polynomial and exponential stability results using novel estimates and auxiliary functions.

Contribution

It introduces new stability analysis methods for p-Laplacian wave equations in moving boundary domains, including polynomial and exponential stability results.

Findings

Polynomial stability for p > 2

Exponential stability for p = 2

New estimates for time-varying coefficients

Abstract

This paper is devoted to studying the stability of p-Laplacian wave equations with strong damping in non-cylindrical domains. The method of proof based on some estimates for time-varying coefficients rising from moving boundary and a modified Kormonik inequality. Meanwhile, by selecting appropriate auxiliary functions, finally we obtain the polynomial stability (p > 2) and exponential stability (p = 2) for such systems in some unbounded development domains.