关于仅具有由Gurtin-Pipkin定律给出的热耗散的多孔热弹性系统的时间行为
On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin-Pipkin law
AI总结：
本文研究仅含Gurtin-Pipkin热耗散的多孔热弹性系统，利用半群方法证明解的存在唯一性，并通过稳定性数$χ_g$给出指数稳定性的充要条件，推广了Fourier和Cattaneo定律下的已有结果。
摘要：
本文考虑一个多孔热弹性系统，该系统仅具有一个由热传导产生的耗散机制，且热传导由Gurtin-Pipkin热定律建模。通过使用半群方法和Lumer-Phillips定理，我们证明了解的存在唯一性。我们引入了一个依赖于系统系数的稳定性数$χ_g$，并在$χ_g=0$的条件下建立了指数稳定性结果。否则，若$χ_g\ e 0$，我们证明指数衰减的缺失。我们的结果改进并推广了文献中先前针对Fourier热传导定律和Cattaneo热传导定律所获得的结果。
英文摘要：
In the present paper we consider a porous thermoelastic system with only one dissipative mechanism generated by the heat conductivity modelled by the Gurtin-Pipkin thermal law. By the use of a semigroup approach and the Lumer-Phillips theorem we prove the existence of a unique solution. We introduce a stability number $χ_g$ depends on the coefficients of the system, and establish an exponential stability result provided that $χ_g=0$. Otherwise, if $χ_g\ne 0$, we prove the lack of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier's and Cattaneo's laws of thermal conductivity.
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