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arXiv · 2503.01527

$L^p-L^q$ estimates for the dissipative and conservative Moore-Gibson-Thompson equations

Wenhui Chen·Mengjun Ma·Xulong Qin
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Abstract

This paper studies some $L^p-L^q$ estimates for the dissipative or conservative Moore-Gibson-Thompson (MGT) equations in the whole space $\mathbb{R}^n$. Our contributions are twofold. By applying the Fourier analysis associated with the modified Bessel function in the dissipative case, we derive some $L^p-L^q$ estimates of solutions. Then, introducing a good unknown related to the free wave equation in the conservative case, some $L^p-L^q$ estimates of solutions with the admissible closed triangle range of exponents are deduced. These results show some essential influences of dissipation from the MGT equations in the $L^q$ framework.

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Wenhui Chen, Mengjun Ma, Xulong Qin. 2025-03-03. $L^p-L^q$ estimates for the dissipative and conservative Moore-Gibson-Thompson equations. https://doi.org/10.1063/5.0270613

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