Journal
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume 17, Issue 3, Pages 959-985Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2018047
Keywords
Nonlinear stability; nonlinear conservation laws; non-convex nonlinearity; rate of decay; weighted energy estimates; image processing
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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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