We study the decay property for symmetric hyperbolic systems with memory-type diffusion. Under the structural condition (called Craftsmanship condition) we prove that the system is uniformly dissipative and the solutions satisfy the corresponding decay property. Our proof is based on a technical energy method in the Fourier space which makes use of the properties of strongly positive definite kernels.

中文翻译：

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具有记忆型扩散的对称双曲系统的衰减特性

我们研究具有记忆型扩散的对称双曲系统的衰减特性。在结构条件下（称为工艺条件），我们证明了系统是均匀耗散的，并且解满足相应的衰减特性。我们的证明是基于傅立叶空间中的一种技术能量方法，该方法利用了强正定核的性质。