Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation
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. Th...
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MDPI AG
2017-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/9/440 |
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doaj-025019152bc444fa8a1808b2f99985022020-11-25T00:46:08ZengMDPI AGEntropy1099-43002017-08-0119944010.3390/e19090440e19090440Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle ViolationKonstantin Zhukovsky0Department of Theoretical Physics, Faculty of Physics, M.V.Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, RussiaHeat 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.https://www.mdpi.com/1099-4300/19/9/440heat conductionGuyer–Krumhansl equationexact analytical solutionmaximum principlenegative solution |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Konstantin Zhukovsky |
| spellingShingle |
Konstantin Zhukovsky Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation Entropy heat conduction Guyer–Krumhansl equation exact analytical solution maximum principle negative solution |
| author_facet |
Konstantin Zhukovsky |
| author_sort |
Konstantin Zhukovsky |
| title |
Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation |
| title_short |
Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation |
| title_full |
Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation |
| title_fullStr |
Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation |
| title_full_unstemmed |
Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation |
| title_sort |
exact negative solutions for guyer–krumhansl type equation and the maximum principle violation |
| publisher |
MDPI AG |
| series |
Entropy |
| issn |
1099-4300 |
| publishDate |
2017-08-01 |
| description |
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. |
| topic |
heat conduction Guyer–Krumhansl equation exact analytical solution maximum principle negative solution |
| url |
https://www.mdpi.com/1099-4300/19/9/440 |
| work_keys_str_mv |
AT konstantinzhukovsky exactnegativesolutionsforguyerkrumhansltypeequationandthemaximumprincipleviolation |
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