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This article is cited in 2 scientific papers (total in 2 papers)
Exact and approximate solutions of a problem with a special feature for a convection-diffusion equation
A. L. Kazakova, L. F. Spevakb a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, 664033, Irkutsk, Russia
b Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, 620049, Yekaterinburg, Russia
Abstract:
Solutions to a nonlinear parabolic convection-diffusion equation are constructed in the form of a diffusion wave that propagates over a zero background with a finite velocity. The theorem of existence and uniqueness of the solution is proven. The solution is constructed in the form of a characteristic series whose coefficients are determined using a recurrent procedure. Exact solutions of the considered type and their characteristics, including the domain of existence, are found, and the behavior of these solutions on its boundaries is studied. The boundary element method and the dual reciprocity method are used to develop, implement, and test an algorithm for constructing approximate solutions.
Keywords:
nonlinear convection-diffusion equation, diffusion wave, characteristic series, exact solution, boundary element method.
Received: 28.09.2020 Revised: 28.09.2020 Accepted: 26.10.2020
Citation:
A. L. Kazakov, L. F. Spevak, “Exact and approximate solutions of a problem with a special feature for a convection-diffusion equation”, Prikl. Mekh. Tekh. Fiz., 62:1 (2021), 22–31; J. Appl. Mech. Tech. Phys., 62:1 (2021), 18–26
Linking options:
https://www.mathnet.ru/eng/pmtf204 https://www.mathnet.ru/eng/pmtf/v62/i1/p22
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Abstract page: | 39 | First page: | 4 |
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