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arXiv · 2507.01538

Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation

Mostafa Meliani·Belkacem Said-Houari
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Abstract

In nonlinear acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In the literature, these families of equations came to be known as Jordan--Moore--Gibson--Thompson (JMGT) models. In this work, we show the global existence of solutions relying only on minimal assumptions on the nonlocal damping kernel. In particular, our result covers the until-now open question of global existence of solutions for the fractionally damped JMGT model with quadratic gradient nonlinearity. The factional damping setting forces us to work with non-integrable kernels, which require a tailored approach in the analysis to control. This approach relies on exploiting the specific nonlinearity structure combined with a weak damping provided by the nonlocality kernel.

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Mostafa Meliani, Belkacem Said-Houari. 2025-07-02. Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation. https://arxiv.org/abs/2507.01538

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