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Conditional Lie–Bäcklund symmetries and functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations

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  • Feng, Wei
  • Ji, Lina
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    Abstract

    The functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations are studied by applying the conditional Lie–Bäcklund symmetry method. A complete list of canonical forms for such equations are presented. Exact solutions to the resulting equations are constructed. The asymptotic behaviors and blow-up properties of some solutions are also discussed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 392 (2013)
    Issue (Month): 4 ()
    Pages: 618-627

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    Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:618-627

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    Keywords: Conditional Lie–Bäcklund symmetry; Functionally separable solution; Generalized inhomogeneous nonlinear diffusion equation; Symmetry reduction;

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    1. Khater, A.H. & Moussa, M.H.M. & Abdul-Aziz, S.F., 2002. "Potential symmetries and invariant solutions for the inhomogeneous nonlinear diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 99-108.
    2. Sophocleous, Christodoulos, 2005. "Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 457-471.
    3. Ivanova, N.M. & Popovych, R.O. & Sophocleous, C. & Vaneeva, O.O., 2009. "Conservation laws and hierarchies of potential symmetries for certain diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 343-356.
    4. Sophocleous, Christodoulos, 2003. "Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 509-529.
    5. Sophocleous, Christodoulos, 2003. "Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 169-183.
    6. Ji, Lina, 2010. "Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5655-5661.
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