Analytical and Numerical Construction of Heat Wave Type Solutions to the Nonlinear Heat Equation with a Source
- Authors: Kazakov A.L.1, Kuznetsov P.A.1, Spevak L.F.2
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory SB RAS
- Institute of Engineering Science UB RAS
- Issue: Vol 239, No 2 (2019)
- Pages: 111-122
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242638
- DOI: https://doi.org/10.1007/s10958-019-04294-x
- ID: 242638
Cite item
Abstract
For a nonlinear parabolic heat equation we construct a heat wave type solution composed of the zero and nonnegative solutions joined continuously along the wave front. We prove the existence and uniqueness of an analytic solution to the problem with a given wave front in the cases of plane, circular, and spherical symmetry. The solution is constructed in the form of a characteristic series with recurrently defined coefficients. In the case of a power source, we show that the original problem can be reduced to the Cauchy problem for a second order ordinary differential equation and the solution is invariant. We present numerical results verified by using the constructed analytic solutions.
About the authors
A. L. Kazakov
Matrosov Institute for System Dynamics and Control Theory SB RAS
Email: pav_ku@mail.ru
Russian Federation, 134, Lermontov St, Irkutsk, 664033
P. A. Kuznetsov
Matrosov Institute for System Dynamics and Control Theory SB RAS
Author for correspondence.
Email: pav_ku@mail.ru
Russian Federation, 134, Lermontov St, Irkutsk, 664033
L. F. Spevak
Institute of Engineering Science UB RAS
Email: pav_ku@mail.ru
Russian Federation, 91, Pervomaiskaya St, Ekaterinburg, 620219