Blow up results for semi-linear structural damped wave model with nonlinear memory

Abstract

This article is to study the nonexistence of global solutions to semi-linear structurally damped wave equation with nonlinear memory in ${\mathbb{R}}^n$ for any space dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to the positivity assumption. We intend to apply the method of a modified test function to establish blow-up results and to overcome some difficulties as well caused by the well-known fractional Laplacian $(-\Delta {)}^{\sigma /2}$ in structural damping terms.

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