Analytical and Numerical Construction of Heat Wave Type Solutions to the Nonlinear Heat Equation with a Source
- 作者: Kazakov A.1, Kuznetsov P.1, Spevak L.2
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隶属关系:
- Matrosov Institute for System Dynamics and Control Theory SB RAS
- Institute of Engineering Science UB RAS
- 期: 卷 239, 编号 2 (2019)
- 页面: 111-122
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242638
- DOI: https://doi.org/10.1007/s10958-019-04294-x
- ID: 242638
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详细
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.
作者简介
A. Kazakov
Matrosov Institute for System Dynamics and Control Theory SB RAS
Email: pav_ku@mail.ru
俄罗斯联邦, 134, Lermontov St, Irkutsk, 664033
P. Kuznetsov
Matrosov Institute for System Dynamics and Control Theory SB RAS
编辑信件的主要联系方式.
Email: pav_ku@mail.ru
俄罗斯联邦, 134, Lermontov St, Irkutsk, 664033
L. Spevak
Institute of Engineering Science UB RAS
Email: pav_ku@mail.ru
俄罗斯联邦, 91, Pervomaiskaya St, Ekaterinburg, 620219