Journal ArticleDOI
Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
TLDR
In this article, it was shown that the nonlinear diffusion equation can be reduced to Fujita's equation if it admits a class of generalized conditional symmetry, and some new exact solutions for a number of important non-linear diffusion equations are obtained.Abstract:
In this paper, we discuss the reduction to Fujita's equation for the nonlinear diffusion equation under certain types of generalized conditional symmetry. It is shown that the nonlinear diffusion equation can be reduced to Fujita's equation if it admits a class of generalized conditional symmetry. As the results, some new exact solutions for a number of important nonlinear diffusion equations are obtained. Many of the solutions obtained here are illustrated graphically with particular reference to the phenomena of extinction, periodic property, blow-up and asymptotical behaviour.read more
Citations
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Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source
TL;DR: In this paper, the generalized conditional symmetry approach is used to study the separation of variables of quasilinear diffusion equations with nonlinear source, and a complete list of canonical forms for such equations which admit the functionally separable solutions is obtained.
Journal ArticleDOI
The variational iteration method: A powerful scheme for handling linear and nonlinear diffusion equations
TL;DR: This work introduces a framework for obtaining exact solutions to linear and nonlinear diffusion equations for some diffusion processes of power law diffusitivies.
Journal ArticleDOI
Separation of variables of a generalized porous medium equation with nonlinear source
TL;DR: In this article, the functional separation of variables of the porous medium equation is studied by using the generalized conditional symmetry approach, and a complete list of canonical forms for such equations which admit the functional separable solutions is obtained.
Journal ArticleDOI
Exact solutions to nonlinear diffusion equations obtained by the decomposition method
TL;DR: A framework to obtain exact solutions to the nonlinear diffusion equations by employing the Adomian decomposition method is developed and is capable of greatly reducing the size of computational domain.
Journal ArticleDOI
New variable separation approach: application to nonlinear diffusion equations
TL;DR: The derivative-dependent functional separable solution (DDFSS) as discussed by the authors is a generalization of the functional-separable solution for nonlinear diffusion equations, which is used to discuss the generalized non-linear diffusion equation based on the generalized conditional symmetry approach.
References
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Journal ArticleDOI
Theory of Thermal Grooving
TL;DR: In this paper, the Gibbs-Thompson formula is used to describe the development of surface grooves at the grain boundaries of a heated polycrystal and the mechanisms of evaporation-condensation and surface diffusion are discussed with the use of the Gibbs•Thompson formula.
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The heat equation shrinking convex plane curves
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Nonlinear Partial Differential Equations in Engineering
W. F. Ames,J. Gillis +1 more