Calculus of Variations and Geometric Measure Theory
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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 14 Dec 2009


Submitted Paper

Inserted: 28 mar 2008
Last Updated: 14 dec 2009

Year: 2008


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.


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