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Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions

Tom 93 / 2011

Roman Cherniha, Oleksii Pliukhin Banach Center Publications 93 (2011), 105-115 MSC: Primary 35Q92; Secondary 22E70 DOI: 10.4064/bc93-0-9

Streszczenie

New $Q$-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions is presented.

Autorzy

  • Roman ChernihaInstitute of Mathematics
    Ukrainian National Academy of Sciences
    Tereshchenkivs'ka Street 3
    Kyiv 01601, Ukraine
    and
    Department of Mathematics
    National University
    `Kyiv-Mohyla Academy'
    Skovoroda Street 2,
    Kyiv 04070, Ukraine
    e-mail
  • Oleksii PliukhinDepartment of Mathematics
    National Technical University
    Pershotravnevyi Prospekt 24
    Poltava, Ukraine
    e-mail

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