In this note, two aspects in the theory of heat conduction model with memory-dependent derivatives (MDDs) are studied. First, the discontinuity solutions of the memory-dependent generalized thermoelasticity model are analyzed. 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 analyzed the nature of the waves and discontinuity of the solutions. Second, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed.
A Note on the Generalized Thermoelasticity Theory With Memory-Dependent Derivatives
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 19, 2016; final manuscript received April 11, 2017; published online May 9, 2017. Assoc. Editor: George S. Dulikravich.
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Shaw, S. (May 9, 2017). "A Note on the Generalized Thermoelasticity Theory With Memory-Dependent Derivatives." ASME. J. Heat Transfer. September 2017; 139(9): 092005. https://doi.org/10.1115/1.4036461
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