Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2021, Volume 196, Pages 36–43
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
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.
nonlinear heat equation, exact solution, existence theorem, uniqueness theorem, series, convergence, boundary-element method
|Russian Foundation for Basic Research
|This work was supported by the Russian Foundation for Basic Research and the Ministry of Science and Technology of Taiwan (project Nos. 20-07-00407 and 20-51-S52003).
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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. Ser. Sovrem. Mat. Pril. Temat. Obz., 196, VINITI, Moscow, 2021, 36–43
Citation in format AMSBIB
\by A.~L.~Kazakov, P.~A.~Kuznetsov, L.~F.~Spevak
\paper On solutions of the traveling wave type for the nonlinear heat equation
\inbook Differential Equations and Optimal Control
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
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