Qualitative study for the p-Laplacian type diffusion-convection equation with the effect of an absorption source

Within this paper, we study the initial growth of interfaces and asymptotic locally weak solutions by the construction of its self-similar solution to the Cauchy Problem for a parabolic p-Laplacian type diffusion-convection equation with the effect of absorption source. The significant methods are applied in this work, techniques of blowing up, rescaling, and comparison principles in non-smooth domains. The importance of this model came through its applications in a variety of fields such as chemical process design, biophysics, plasma physics, quantum physics, and others.

Keywords:

p-Laplacian diffusion equation , rescaling technique , self-similarity , weak solution , interface