Journal article
STABILITY OF TRAVELING WAVES OF MODELS FOR IMAGE PROCESSING WITH NON-CONVEX NONLINEARITY
Communications on pure and applied analysis, Vol.17(3), pp.959-985
05/01/2018
DOI: 10.3934/cpaa.2018047
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.
Details
- Title: Subtitle
- STABILITY OF TRAVELING WAVES OF MODELS FOR IMAGE PROCESSING WITH NON-CONVEX NONLINEARITY
- Creators
- Tong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAJeungeun Park - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Communications on pure and applied analysis, Vol.17(3), pp.959-985
- DOI
- 10.3934/cpaa.2018047
- ISSN
- 1534-0392
- eISSN
- 1553-5258
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Number of pages
- 27
- Language
- English
- Date published
- 05/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241157602771
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