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This article is cited in 1 scientific paper (total in 1 paper)
On solutions of the traveling wave type for the nonlinear heat equation
A. L. Kazakova, P. A. Kuznetsova, L. F. Spevakb a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
b Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg
Abstract:
In this paper, we consider the problem of finding solutions to a nonlinear heat equation with a power-law nonlinearity, which have the form of a traveling wave and simulate the propagation of disturbances along a cold background with a finite speed. We show that the construction can be reduced to the Cauchy problem for a second-order ordinary differential equation with a singular coefficient of the highest derivative. For this Cauchy problem, the theorem on the existence and uniqueness of a smooth solution is proved. We develop an algorithm for constructing an approximate solution based on the boundary-element method and also present the results of computational experiments with numerical estimates of the parameters of the solution.
Keywords:
nonlinear heat equation, exact solution, existence theorem, uniqueness theorem, series, convergence, boundary-element method.
Citation:
A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “On solutions of the traveling wave type for the nonlinear heat equation”, Differential Equations and Optimal Control, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 196, VINITI, Moscow, 2021, 36–43
Linking options:
https://www.mathnet.ru/eng/into847 https://www.mathnet.ru/eng/into/v196/p36
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Abstract page: | 171 | Full-text PDF : | 78 | References: | 24 |
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