Journal article
STABILITY OF TRAVELING WAVE SOLUTIONS OF NONLINEAR CONSERVATION LAWS FOR IMAGE PROCESSING
Communications in mathematical sciences, Vol.15(4), pp.1073-1106
01/01/2017
DOI: 10.4310/CMS.2017.v15.n4.a8
Abstract
This paper studies the stability of smooth traveling wave solutions to a nonlinear PDE problem in reducing image noise. Specifically, we prove that the solution to the Cauchy problem approaches to the traveling wave solution if the initial data is a small perturbation of the traveling wave. We use a weighted energy method to show that if the initial perturbation decays algebraically or exponentially as vertical bar x vertical bar -> infinity, then the Cauchy problem solution approaches to the traveling wave at corresponding rates as t -> infinity.
Details
- Title: Subtitle
- STABILITY OF TRAVELING WAVE SOLUTIONS OF NONLINEAR CONSERVATION LAWS FOR IMAGE PROCESSING
- 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 in mathematical sciences, Vol.15(4), pp.1073-1106
- Publisher
- INT PRESS BOSTON, INC
- DOI
- 10.4310/CMS.2017.v15.n4.a8
- ISSN
- 1539-6746
- eISSN
- 1945-0796
- Number of pages
- 34
- Language
- English
- Date published
- 01/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984241154302771
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