Stability of traveling waves of models for image processing with non-convex nonlinearity

Tong Li; Jeungeun Park

doi:10.3934/cpaa.2018047

Article Contents

2018, Volume 17, Issue 3: 959-985. Doi: 10.3934/cpaa.2018047

This issue Previous Article Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval Next Article Non-existence of global solutions to nonlinear wave equations with positive initial energy

Stability of traveling waves of models for image processing with non-convex nonlinearity

Tong Li^, and
Jeungeun Park

Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA

* Corresponding author: Tong Li
* Corresponding author: Tong Li

Received: August 31, 2017

Revised: August 31, 2017

Published: May 2018

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Abstract

We establish the existence and stability of smooth large-amplitude traveling waves to nonlinear conservation laws modeling image processing with general flux functions. We innovatively construct a weight function in the weighted energy estimates to overcome the difficulties caused by the absence of the convexity of fluxes in our model. Moreover, we prove that if the integral of the initial perturbation decays algebraically or exponentially in space, the solution converges to the traveling waves with rates in time, respectively. Furthermore, we are able to construct another new weight function to deal with the degeneracy of fluxes in establishing the stability.

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Mathematics Subject Classification: Primary: 35B35, 35B40, 35B45, 35C07, 35L65; Secondary: 68U10.

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