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

2020/02/16 by Dao, Tuan Anh, Fino, Ahmad Z. · 1 citation
#26A33 #35A01 #35B33 #35L71 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.06582

Abstract

This article is to study the nonexistence of global solutions to semi-linear structurally damped wave equation with nonlinear memory in \Rⁿ for any space dimensions n≥ 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 (-Δ)^σ/2 in structural damping terms.

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