Rate of convergence for one-dimensional quasilinear parabolic problem and its applications

TL;DR

This paper establishes an exponential convergence rate for solutions to a class of one-dimensional quasilinear parabolic equations using a comparison principle, with applications in population dynamics and image processing.

Contribution

It introduces a novel exponential convergence rate for these equations and applies it to practical models in biology and image analysis.

Findings

Exponential convergence rate derived for solutions

Application to population dynamics models

Application to image processing models

Abstract

Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in one space dimension. We then apply the result to some models in population dynamics and image processing.