Development of Interfaces in Nonlinear Multidimensional Reaction-Diffusion Equations With Parabolic p-Laplacian Properties

This research examines the behavior of interfaces in nonlinear multidimensional reaction–diffusion equations with parabolic p-Laplacian properties, which are applicable across a wide range of biological, physical, and chemical contexts. The value of this work lies in its contribution to understanding how interfaces behave under slow diffusion, shedding light on the complex interplay between diffusion and reaction forces. The study aims to analyze the existence and dynamics of interfaces governed by a Cauchy problem, particularly focusing on their expansion, contraction, or stability, influenced by different system parameters. The methodology incorporates the formulation of weak solutions, rescaling techniques, and self-similar solutions to derive detailed expressions for the local interface behavior. The main conclusion is that the behavior of the interface, whether it expands, contracts, or remains stable, is strongly governed by the parameters p, λ, and q. Additionally, the finite propagation speed ensures that the effects are confined, making the model applicable to practical scenarios such as tumor growth, porous media flow, and phase transitions.