The singular limit of a haptotaxis model with bistable growth

TL;DR

This paper analyzes the singular limit of a haptotaxis model with bistable growth, showing how interface motion depends on curvature and nonlocal haptotaxis effects, with results valid for general initial data.

Contribution

It establishes the singular limit of the model and characterizes the resulting interface motion, including the effects of nonlocal haptotaxis terms.

Findings

Interface velocity depends on mean curvature and nonlocal haptotaxis term.

Generated interface occurs in small time for general initial data.

Provides a rigorous mathematical framework for the singular limit.

Abstract

We consider a model for haptotaxis with bistable growth and study its singular limit. This yiels an interface motion where the normal velocity of the interface depends on the mean curvature and on some nonlocal haptotaxis term. We prove the result for general initial data after establishing a result about generation of interface in a small time.