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

  • Kewei ZhangEmail author
Original Article


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.


Perona-Malik model One-dimensional Infinitely many solutions Differential inclusion Relaxation property 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK

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