We introduce and analyze a new, nonlinear fourth-order regularization of forward-backward parabolic equations. In one space dimension, under general assumptions on the potentials, which include those of Perona-Malik type, we prove existence of Radon measure-valued solutions under both natural and essential boundary conditions. If the decay at infinity of the nonlinearities is sufficiently fast, we also exhibit examples of local solutions whose atomic part arises and/or persists (in contrast to the linear fourth-order regularization) and even disappears within finite time (in contrast to pseudoparabolic regularizations).

Bertsch, M., Giacomelli, L., Tesei, A. (2019). Measure-valued solutions to a nonlinear fourth-order regularization of forward-backward parabolic equations. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51(1), 374-402 [10.1137/18M1203821].

Measure-valued solutions to a nonlinear fourth-order regularization of forward-backward parabolic equations

Bertsch M.
;
Giacomelli L.;Tesei A.
2019-01-01

Abstract

We introduce and analyze a new, nonlinear fourth-order regularization of forward-backward parabolic equations. In one space dimension, under general assumptions on the potentials, which include those of Perona-Malik type, we prove existence of Radon measure-valued solutions under both natural and essential boundary conditions. If the decay at infinity of the nonlinearities is sufficiently fast, we also exhibit examples of local solutions whose atomic part arises and/or persists (in contrast to the linear fourth-order regularization) and even disappears within finite time (in contrast to pseudoparabolic regularizations).
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
forward-backward parabolic equations; fourth-order parabolic equations; Radon measures; Perona-Malik equation
Bertsch, M., Giacomelli, L., Tesei, A. (2019). Measure-valued solutions to a nonlinear fourth-order regularization of forward-backward parabolic equations. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51(1), 374-402 [10.1137/18M1203821].
Bertsch, M; Giacomelli, L; Tesei, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215056
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