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.

Paolini, M., Bellettini, G., Novaga, M., Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension, <<MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES>>, 2011; 21 (2): 241-265 [http://hdl.handle.net/10807/8935]

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

Paolini, Maurizio;Bellettini, Giovanni;Novaga, Matteo
2011

Abstract

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.
Inglese
Paolini, M., Bellettini, G., Novaga, M., Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension, <<MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES>>, 2011; 21 (2): 241-265 [http://hdl.handle.net/10807/8935]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/8935
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