A class of moving boundary problems with an exponential source term

TL;DR

This paper studies a class of moving boundary problems with exponential source terms, connecting them to Stefan problems and deriving explicit similarity solutions to better understand their dynamics.

Contribution

It introduces a novel approach using reciprocal and Cole-Hopf transformations to analyze nonlinear moving boundary problems with exponential sources.

Findings

Derived explicit similarity solutions in parametric form.

Established a connection to Stefan-type problems under various boundary conditions.

Enhanced understanding of the dynamics of nonlinear moving boundary problems.

Abstract

This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed face, through the application of a reciprocal transformation alongside the Cole-Hopf transformation. For specific cases, we derive explicit similarity solutions in parametric form. This innovative approach enhances our understanding of the underlying dynamics and offers valuable insights into the behavior of these systems.