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.
|Numero di pagine
|Mathematical Models and Methods in Applied Sciences
|Stato di pubblicazione
|Pubblicato - 2011
- ill-posed problems
- image segmentation
- partial differential equations