Series solution for porous medium equation with a source term by Adomian's decomposition method

In this paper, we consider the cauchy problem for a porous medium equation with a source term. This equation has been widely used as a simple model for a nonlinear heat propagation in a reactive medium [C. Gui, X. Kang, Localization for a porous medium type equation in high dimensions, Transactions of the American Mathematical Society 356 (11) (2004) 4273-4285]. We obtain a series solution of porous media equation with a source term by using Adomian decomposition Method (ADM) [G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994].