# Interfacial behaviors of the backward forward diffusion convection equations

## TL;DR

This paper investigates the interfacial dynamics of backward forward diffusion convection equations, showing how the regions evolve over time assuming classical solutions exist in one dimension.

## Contribution

It provides a theoretical analysis of the interfacial behavior, demonstrating the shrinking of backward regions and expansion of forward regions with positive rates.

## Key findings

- Backward region shrinks over time
- Forward region expands over time
- Results assume classical solutions in one dimension

## Abstract

This paper is devoted to the interfacial behaviors of a class of backward forward diffusion convection equations. Under the assumption that the equations have classical solutions in one dimension, we prove that the backward region shrinks and the forward region expands with a positive rate.