On the decay of solutions of a damped quasilinear wave equation with variable‐exponent nonlinearities

Abstract

In this work, we consider the following nonlinear wave equation with variable exponents:where Ω is a bounded domain, T > 0, and m(.) and r(.) are continuous functions. We will establish several decay results depending on the range of the variable exponents m and r.KEYWORDS exponential decay, polynomial decay, strong damping, variable exponent, wave MSC CLASSIFICATION 35B35; 35L20; 35L70in a bounded domain Ω, with a smooth boundary, was considered at a large scale. For instance, Nakao 6 looked into Equation (1.2), in the case when (u) = |u| p−2 u, and g(u t ) = |u t | m−2 u t , m, p > 2 and proved a unique global weak solution if 2 ≤ p ≤ 2(n − 1)∕(n − 2), n ≥ 3 and a global unique strong solution if p > 2(n − 1)∕(n − 2), n ≥ 3. Moreover, he addressed Math Meth Appl Sci. 2020;43:5114-5126. wileyonlinelibrary.com/journal/mma

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