Existence of infinitely many solutions for the one-dimensional Perona-Malik model
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- Zhang, K. Calc. Var. (2006) 26: 171. doi:10.1007/s00526-005-0363-4
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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.