Propagation of nonlinear thermoelastic waves in porous media within the theory of heat conduction with memory: physical derivation and exact solutions

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• 作者：Roberto Garra
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：40
• 期：4
• 页码：1307-1315
• 全文大小：182K
• ISSN：1099-1476

文摘

In this paper, we study a mathematical model of nonlinear thermoelastic wave propagation in fluid-saturated porous media, considering memory effect in the heat propagation. In particular, we derive the governing equations in one dimension by using the Gurtin–Pipkin theory of heat flux history model and specializing the relaxation function in such a way to obtain a fractional Erdélyi–Kober integral. In this way, we obtain a nonlinear model in the framework of time-fractional thermoelasticity, and we find an explicit analytical solution by means of the invariant subspace method. A second memory effect that can play a significant role in this class of models is parametrized by a generalized time-fractional Darcy law. We study the equations obtained also in this case and find an explicit traveling wave type solution. Copyright