ANALYTICAL AND NUMERICAL SOLUTIONS TO THE PROBLEM OF DIFFUSION WAVE INITIATION FOR A QUASILINEAR PARABOLIC SYSTEM
A. L. Kazakov1,2, L. F. Spevak2
1Institute of System Dynamics and Control Theory, V. M. Matrosov Institute SB RAS, Irkutsk, Russia
2E. S. Gorkunov Institute of Machine Science, Ural Branch of RAS, Yekaterinburg, Russia
Keywords: nonlinear parabolic system, diffusion wave, existence theorem, exact solution, numerical method
Abstract
Solutions of the diffusion wave type are constructed and analyzed for a system of two degenerate nonlinear parabolic equations. The problem of initiating a diffusion wave is considered for an arbitrary form of nonlinearity in the system and for arbitrary directions of motion of the zero fronts of the two target functions. A theorem is proved on the existence of four different analytical solutions depending on the propagation directions of the zero fronts. A new numerical method is proposed, which for the first time enables the solution of the problem for the case of oppositely directed motion of the two zero fronts. A new exact solution is explicitly constructed and used to verify the computational results. A numerical experiment is performed, demonstrating the convergence of the numerical method and its effectiveness across various problem parameters.
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