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

TL;DR

This paper analyzes a modified telegraph-type heat conduction model with self-similar solutions, exploring its mathematical structure and deriving additional solutions for various parameters, building on previous work with a focus on rich special function solutions.

Contribution

It provides a detailed analysis of a non-autonomous telegraph-type heat equation with self-similar solutions, expanding understanding of its mathematical properties and solution space.

Findings

Rich mathematical structure due to special functions

Additional analytic solutions for various parameters

Self-similar solutions with desirable properties

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.