Conditional Lie–Bäcklund symmetries and invariant subspaces to nonlinear diffusion equations with source

2012 ◽  
Vol 391 (24) ◽  
pp. 6320-6331 ◽  
Author(s):  
Lina Ji
Keyword(s):  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations

scholarly journals Conditional Lie-Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Junquan Song ◽  
Yujian Ye ◽  
Danda Zhang ◽  
Jun Zhang
Keyword(s):  
Invariant Subspace ◽  
Dynamic Systems ◽  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Higher Order ◽  
Diffusion Equations ◽  
Canonical Forms ◽  
Nonlinear Diffusion Equations ◽  
Symmetry Approach ◽  
Finite Dimensional

Conditional Lie-Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with sourceut=e−qx(epxP(u)uxm)x+Q(x,u),m≠1. We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie-Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamic systems.

scholarly journals The Neumann problem for nonlocal nonlinear diffusion equations

2007 ◽  
Vol 8 (1) ◽  
pp. 189-215 ◽  
Author(s):  
Fuensanta Andreu ◽  
José M. Mazón ◽  
Julio D. Rossi ◽  
Julián Toledo
Keyword(s):  
Neumann Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
The Neumann Problem ◽  
Nonlocal Nonlinear
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