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May  2018, 17(3): 959-985. doi: 10.3934/cpaa.2018047

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

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

* Corresponding author: Tong Li

Received  September 2017 Revised  September 2017 Published  January 2018

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.

Citation: Tong Li, Jeungeun Park. Stability of traveling waves of models for image processing with non-convex nonlinearity. Communications on Pure & Applied Analysis, 2018, 17 (3) : 959-985. doi: 10.3934/cpaa.2018047
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