The Rate at Which the Energy of Solutions for a Class of p-Laplacian Wave Equation Decays

Abstract EN

We will investigate the decay estimate of the energy of the global solutions to the p-Laplacian wave equation with dissipation of the form utt-div (∇xup-2∇xu)+σ(t)(ut-div (∇xutm-2∇xut))=0 under suitable assumptions on the positive function σ.

For this end we use the multiplier method combined with nonlinear integral inequalities given by Martinez; the proof is based on the construction of a special weight function that depends on the behavior of σ.