Heat conduction: a telegraph-type model with self-similar behavior of solutions II

Abstract

In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type heat conduction equation which has desirable self-similar solution. Now we present a detailed in-depth analysis of this model and discuss additional analytic solutions for different parameters. The solutions have a very rich and interesting mathematical structure due to various special functions.

12 pages, 10 figures 3 of them are colour, we plan to submit it to J. Phys. A: Math. Theor

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