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Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation

Department of Theoretical Physics, Faculty of Physics, M.V.Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia
Entropy 2017, 19(9), 440; https://doi.org/10.3390/e19090440
Received: 22 July 2017 / Revised: 17 August 2017 / Accepted: 21 August 2017 / Published: 24 August 2017
(This article belongs to the Special Issue Selected Papers from 14th Joint European Thermodynamics Conference)
Heat propagation in the Guyer–Krumhansl model is studied. The exact analytical solutions for the one-dimensional Guyer–Krumhansl equation are obtained. The operational formalism is employed. Some examples of initial functions are considered, modeling various initial heat pulses and distributions. The effect of the ballistic heat transfer in an over–diffusive regime is elucidated. The behavior of the solutions in such a regime is explored. The maximum principle and its violation for the obtained solutions are discussed in the framework of heat conduction. Examples of negative solutions for the Guyer–Krumhansl equation are demonstrated. View Full-Text
Keywords: heat conduction; Guyer–Krumhansl equation; exact analytical solution; maximum principle; negative solution heat conduction; Guyer–Krumhansl equation; exact analytical solution; maximum principle; negative solution
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Zhukovsky, K. Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation. Entropy 2017, 19, 440.

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