scholarly journals Solutions for nonlinear diffusion equations with integral type boundary conditions

1963 ◽  
Author(s):  
Kenneth Laurel Deckert
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Integral Type ◽  
Nonlinear Diffusion Equations ◽  
Type Boundary

scholarly journals FUJITA CRITICAL CURVE FOR A COUPLED DIFFUSION SYSTEM WITH INHOMOGENEOUS NEUMANN BOUNDARY CONDITIONS∗

2016 ◽  
Vol 21 (2) ◽  
pp. 260-269
Author(s):  
Runmei Du ◽  
Minghao Guo
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Neumann Boundary ◽  
Critical Curve ◽  
Neumann Boundary Conditions ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Exterior Problems ◽  
Coupled Diffusion

In this paper, we establish the blow-up theorems of Fujita type for a class of exterior problems of nonlinear diffusion equations subject to inhomogeneous Neumann boundary conditions. The critical Fujita exponents are determined and it is shown that the critical curve belongs to the blow-up case under any nontrivial initial data.

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

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.

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