Title: $L^p-L^q$ estimates for the dissipative and conservative Moore-Gibson-Thompson equations Show Chinese title

Title: $L^p-L^q$用于耗散和保守的Moore-Gibson-Thompson方程的估计

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. Show Chinese abstract

Abstract: 本文研究了整个空间$\mathbb{R}^n$中耗散或保守的Moore-Gibson-Thompson(MGT)方程的一些$L^p-L^q$估计。 我们的贡献有两个方面。 通过应用与耗散情况下修改的贝塞尔函数相关的傅里叶分析，我们推导出了一些解的$L^p-L^q$估计。 然后，在保守情况下引入与自由波动方程相关的良好未知量，得出了一些在允许闭合三角形指数范围内的解的$L^p-L^q$估计。 这些结果表明了MGT方程在$L^q$框架中耗散的一些基本影响。