Measure-valued solutions to a nonlinear fourth-order regularization of forward-backward parabolic equations
| Autor: | Lorenzo Giacomelli, Michiel Bertsch, Alberto Tesei |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
forward-backward parabolic equations
Applied Mathematics Mathematical analysis Space dimension Forward backward 01 natural sciences Parabolic partial differential equation Regularization (mathematics) 010101 applied mathematics Computational Mathematics Nonlinear system Perona--Malik equation Fourth order fourth-order parabolic equations Radon measures Settore MAT/05 - Analisi Matematica Perona-Malik equation 0101 mathematics Analysis Mathematics |
| Zdroj: | SIAM journal on mathematical analysis 51 (2019): 374–402. doi:10.1137/18M1203821 info:cnr-pdr/source/autori:Bertsch M.; Giacomelli L.; Tesei A./titolo:Measure-valued solutions to a nonlinear fourth-order regularization of forward-backward parabolic equations/doi:10.1137%2F18M1203821/rivista:SIAM journal on mathematical analysis (Print)/anno:2019/pagina_da:374/pagina_a:402/intervallo_pagine:374–402/volume:51 |
| DOI: | 10.1137/18M1203821 |
| Popis: | We introduce and analyze a new, nonlinear fourth-order regularization of forwardbackward 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). |
| Databáze: | OpenAIRE |
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