We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation con-verge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formalasymptotic expansion argument, and on a careful construction of discrete comparison functions. 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.

Bellettini, G., Novaga, M., Paolini, M. (2011). Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 21(2), 1-25 [10.1142/S0218202511005040].

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

BELLETTINI, GIOVANNI;
2011-01-01

Abstract

We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation con-verge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formalasymptotic expansion argument, and on a careful construction of discrete comparison functions. 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.
2011
Bellettini, G., Novaga, M., Paolini, M. (2011). Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 21(2), 1-25 [10.1142/S0218202511005040].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1017459