Exact solutions to nonlinear diffusion equations obtained by the decomposition method. (English) Zbl 1027.35019

Wazwaz, Abdul-Majid

Appl. Math. Comput. 123, No. 1, 109-122 (2001).

Summary: We develop a framework to obtain exact solutions to the nonlinear diffusion equations by employing the Adomian decomposition method. Exact solutions are obtained for some important physical processes of power law diffusivities. The method is capable of greatly reducing the size of computational domain and is presented in a general way so that it can be used in more diffusion classes.

MSC:

35C10	Series solutions to PDEs
35K57	Reaction-diffusion equations

Keywords:

power law diffusivity; Adomian decomposition method; Adomian polynomials; steady-state solution

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