We rigorously 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 comparison functions. Despite the equation having a region where it is backward parabolic, we prove a discrete comparison principle, which is the key tool for the convergence result.
|Autori:||BELLETTINI G; M. NOVAGA; PAOLINI M|
|Titolo:||Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension|
|Anno del prodotto:||2011|
|Digital Object Identifier (DOI):||10.1142/S0218202511005040|
|Appare nelle tipologie:||1.1 Articolo in rivista|