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STABILITY OF TRAVELING WAVES OF MODELS FOR IMAGE PROCESSING WITH NON-CONVEX NONLINEARITY
Journal article   Open access   Peer reviewed

STABILITY OF TRAVELING WAVES OF MODELS FOR IMAGE PROCESSING WITH NON-CONVEX NONLINEARITY

Tong Li and Jeungeun Park
Communications on pure and applied analysis, Vol.17(3), pp.959-985
05/01/2018
DOI: 10.3934/cpaa.2018047
url
https://doi.org/10.3934/cpaa.2018047View
Published (Version of record) Open Access

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.
Mathematics Physical Sciences Mathematics, Applied Science & Technology

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