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Existence of infintely many solutions for the one-dimensional Perona-Malik model

By Kewei Zhang


We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem

Publisher: Springer Verlag
Year: 2006
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