Existence of infinitely many solutions for the one-dimensional Perona-Malik model |
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Authors: | Kewei Zhang |
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Affiliation: | (1) Department of Mathematics, University of Sussex, Brighton, BN1 9R, UK |
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Abstract: | 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. |
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Keywords: | Perona-Malik model One-dimensional Infinitely many solutions Differential inclusion Relaxation property |
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