Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials
dc.bibliographicCitation.date | 2022 | |
dc.bibliographicCitation.firstPage | 3143 | |
dc.bibliographicCitation.journalTitle | Journal of dynamics and differential equations | eng |
dc.bibliographicCitation.lastPage | 3164 | |
dc.bibliographicCitation.volume | 34 | |
dc.contributor.author | Mielke, Alexander | |
dc.date.accessioned | 2022-03-21T07:59:48Z | |
dc.date.available | 2022-03-21T07:59:48Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We consider a non-negative and one-homogeneous energy functional J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional E(t,u)=tJ(u) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/8285 | |
dc.identifier.uri | https://doi.org/10.34657/7323 | |
dc.language.iso | eng | eng |
dc.publisher | New York, NY [u.a.] : Springer Science + Business Media B.V. | eng |
dc.relation.doi | https://doi.org/10.1007/s10884-021-10007-3 | |
dc.relation.essn | 1572-9222 | |
dc.rights.license | CC BY 4.0 Unported | eng |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | eng |
dc.subject.ddc | 510 | eng |
dc.subject.other | Contraction semigroup | eng |
dc.subject.other | Energetic solutions | eng |
dc.subject.other | Gradient flows | eng |
dc.subject.other | Rate-independent systems | eng |
dc.subject.other | Set of stable states | eng |
dc.subject.other | Time reparametrization | eng |
dc.title | Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials | eng |
dc.type | Article | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Zeitschriftenartikel | eng |
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