Siberian Mathematical Journal

, Volume 44, Issue 4, pp 680–685 | Cite as

Properties of the Fast Diffusion Equation and Its Multidimensional Exact Solutions

  • E. I. Semenov


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.

fast diffusion exact multidimensional solution quasilinear parabolic equation Liouville equation conjugate harmonic function 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. I. Semenov
    • 1
  1. 1.Institute of System Dynamics and Control TheoryIrkutsk

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