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

Tuan Anh Dao and Ahmad Z. Fino

Mathematische Nachrichten, 2022, vol. 295, issue 2, 309-322

Abstract: In this article, we study the nonexistence of global solutions to a semi‐linear structurally damped wave equation with nonlinear memory in Rn$\mathbb {R}^n$ for any space dimension n≥1$n\ge 1$ and for the initial arbitrarily data being subject to a positivity assumption. We intend to apply the method of test function to establish blow‐up results and to overcome some difficulties as well caused by the well‐known fractional Laplacian (−Δ)σ/2$(-\Delta )^{\sigma /2}$ in structural damping terms.

Date: 2022
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https://doi.org/10.1002/mana.202000159

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:295:y:2022:i:2:p:309-322

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