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research-article

A note on the generalized thermoelasticity theory with memory dependent derivatives

[+] Author and Article Information
Soumen Shaw

Department of Mathematics, IIEST, Shibpur, India
shaw_soumen@rediffmail.com

1Corresponding author.

ASME doi:10.1115/1.4036461 History: Received November 19, 2016; Revised April 11, 2017

Abstract

In this note, two aspects in the theory of heat conduction model with memory dependent derivatives are studied. Firstly, the discontinuity solutions of the memory dependent generalized thermo-elasticity model is analysed. The fundamental equations of the problem are expressed in the form of a vector matrix differential equation. Applying modal decomposition technique the vector matrix differential equation is solved by eigenvalue approach in Laplace transform domain. In order to obtain the solution in the physical domain an approximate method by using asymptotic expansion is applied for short time domain and analyse the nature of the waves and discontinuity of the solutions. Secondly, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed.

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