Analytical Treatment and Convergence of the Adomian Decomposition Method for Instability Phenomena Arising during Oil Recovery Process

Abstract EN

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.