Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation. Under the assumption that the relaxation kernel decays exponentially, we prove local well-posedness in unbounded two- and three-dimensional domains. In addition, we show that the solution of the three-dimensional model exists globally in time for small and smooth data, while the energy of the system decays polynomially.

中文翻译：

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无界域非线性声波记忆效应和热弛豫的数学分析

受非线性声波通过松弛遗传介质传播的启发，我们研究了非局部三阶 Jordan-Moore-Gibson-Thompson 声波方程。在松弛核呈指数衰减的假设下，我们证明了无界二维和三维域中的局部适定性。此外，我们表明，对于小而平滑的数据，三维模型的解在时间上是全局存在的，而系统的能量以多项式衰减。