On Some Forward-Backward Diffusion Equations

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Abstract

We describe an application of the partial differential inclusion method to the existence of Lipschitz weak solutions for certain forward-backward diffusion equations including the one-dimensional version of the Perona-Malik equation in image processing.

Keywords:

forward-backward diffusion equation;partial differential inclusion;relaxation property;existence of weak solutions;image processing
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On Some Forward-Backward Diffusion Equations. (2006). Journal of Partial Differential Equations, 19(3), 271-288. https://gsp.tricubic.dev/jpde/article/view/4077