Analytical treatment and convergence of the Adomian decomposition method for instability phenomena arising during oil recovery process (Q275929)

Summary: An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model porous medium equation. Moreover, we prove that this decomposition scheme applied to a porous medium equation arising in instability phenomena in double phase flow through porous media is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration.