Invariant Solutions of Nonlinear Diffusion Equations with Maximal Symmetry Algebra
- https://doi.org/10.1142/S1402925111001301How to use a DOI?
- Partial differential equations, Lie symmetries, invariant solutions
Nonlinear n-dimensional second-order diffusion equations admitting maximal Lie algebras of point symmetries are considered. Examples of invariant solutions, as well as of solutions on invariant subspaces for some nonlinear operators, are constructed for arbitrary n. A complete description of all possible types of invariant solutions is given in the case n = 2 for the equation possessing an infinitely dimensional symmetry algebra. The results obtained are generalized for the hyperbolic and other fourth-order parabolic equations of thin film and nonlinear dispersion type.
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Cite this article
TY - JOUR AU - V. A. Galaktionov AU - S. R. Svirshchevskii PY - 2021 DA - 2021/01 TI - Invariant Solutions of Nonlinear Diffusion Equations with Maximal Symmetry Algebra JO - Journal of Nonlinear Mathematical Physics SP - 107 EP - 121 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001301 DO - https://doi.org/10.1142/S1402925111001301 ID - Galaktionov2021 ER -