Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension

G. Bellettini, Maurizio Paolini, M. Novaga, Giovanni Bellettini, Matteo Novaga

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

5 Citazioni (Scopus)


We prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete sub and supersolutions. Despite the equation has a region where it is backward parabolic, we prove a discrete comparison principle, which is the key tool for the convergence result.
Lingua originaleEnglish
pagine (da-a)241-265
Numero di pagine25
RivistaMathematical Models and Methods in Applied Sciences
Stato di pubblicazionePubblicato - 2011


  • Perona-Malik
  • ill-posed problems
  • image segmentation
  • partial differential equations


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