Decay estimates for solutions of evolutionary damped p-Laplace equations

Abstract

In this note, we study the asymptotic behavior, as t tends to infinity, of the solution u to the evolutionary damped p-Laplace equation $$ u_{tt}+ u_t =\Delta_p u $$ with Dirichlet boundary conditions. Let \(u^*\) denote the stationary solution with same boundary values, then we prove the \(W^{1,p}\)-norm of \(u(t) - u^*\) decays for large \(t\) like \(t^{-1/((p-1)p)}\), in the degenerate case \(p\geq 2\). For more information see https://ejde.math.txstate.edu/Volumes/2021/73/abstr.html