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arXiv · 2005.07245

On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity

Vanja Nikolić·Belkacem Said-Houari
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Abstract

We prove global solvability of the third-order in time Jordan-More-Gibson-Thompson acoustic wave equation with memory in $\mathbb{R}^n$, where $n \geq 3$. This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global solvability is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data.

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Vanja Nikolić, Belkacem Said-Houari. 2020-05-14. On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity. https://doi.org/10.1007/s00021-020-00522-6

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