Steady State Solutions of a Mass-Conserving Bistable Equation with a Saturating Flux

TL;DR

This paper analyzes steady state solutions of a mass-conserving bistable equation with a saturating flux, exploring how bifurcation diagrams change with mass and interval length, relevant for phase transition modeling.

Contribution

It introduces a quasilinear analogue of the Rubinstein-Steinberg equation and studies its stationary solutions and bifurcation behavior under varying parameters.

Findings

Bifurcation diagrams depend on mass and interval length.

Stationary solutions exhibit complex bifurcation structures.

The model effectively describes order parameter conserving phase transitions.

Abstract

We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein-Steinberg equation, suitable for description of order parameter conserving solid-solid phase transitions in the case of large spatial gradients in the order parameter. We discuss stationary solutions and investigate the change in bifurcation diagrams as the mass constraint and the length of the interval are varied.