Calculus of Variations and Geometric Measure Theory

G. Bellettini - M. Novaga - M. Paolini

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

created by novaga on 28 Mar 2008
modified on 10 Nov 2018


Published Paper

Inserted: 28 mar 2008
Last Updated: 10 nov 2018

Journal: Math. Mod. Meth. Appl. Sc.
Volume: 21
Number: 2
Pages: 1-25
Year: 2011


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.