Analytical and Numerical Construction of Heat Wave Type Solutions to the Nonlinear Heat Equation with a Source
- Авторлар: Kazakov A.1, Kuznetsov P.1, Spevak L.2
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Мекемелер:
- Matrosov Institute for System Dynamics and Control Theory SB RAS
- Institute of Engineering Science UB RAS
- Шығарылым: Том 239, № 2 (2019)
- Беттер: 111-122
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242638
- DOI: https://doi.org/10.1007/s10958-019-04294-x
- ID: 242638
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
A. Kazakov
Matrosov Institute for System Dynamics and Control Theory SB RAS
Email: pav_ku@mail.ru
Ресей, 134, Lermontov St, Irkutsk, 664033
P. Kuznetsov
Matrosov Institute for System Dynamics and Control Theory SB RAS
Хат алмасуға жауапты Автор.
Email: pav_ku@mail.ru
Ресей, 134, Lermontov St, Irkutsk, 664033
L. Spevak
Institute of Engineering Science UB RAS
Email: pav_ku@mail.ru
Ресей, 91, Pervomaiskaya St, Ekaterinburg, 620219