Exact and Approximate Solutions of a Problem with a Special Feature for a Convection-Diffusion Equation
A. L. Kazakov1, L. F. Spevak2
1Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Irkutsk, 664033, Russia
2Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620049, Russia
Keywords: nonlinear convection-diffusion equation, diffusion wave, characteristic series, exact solution, boundary element method
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.
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