Properties of the Fast Diffusion Equation and Its Multidimensional Exact Solutions |
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Authors: | Semenov E I |
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Institution: | (1) Institute of System Dynamics and Control Theory, Irkutsk |
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Abstract: | We prove invariance of the fast diffusion equation in the two-dimensional coordinate space and give its reduction to a one-dimensional analog in the space variable. Using these results, we construct new exact multidimensional solutions which depend on arbitrary harmonic functions. As a consequence, we obtain new exact solutions to the well-known Liouville equation, the stationary analog of the fast diffusion equation with a linear source. We consider some generalizations to the case of systems of quasilinear parabolic equations. |
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Keywords: | fast diffusion exact multidimensional solution quasilinear parabolic equation Liouville equation conjugate harmonic function |
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