On the Doubly Singular Equation γ(u)t = ∆_pu
| Main Author: | |
|---|---|
| Publication Date: | 2005 |
| Format: | Article |
| Language: | eng |
| Source: | Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| Download full: | https://hdl.handle.net/10348/12448 |
Summary: | We prove that local weak solutions of a nonlinear parabolic equation with a doubly singular character are locally continuous. One singularity occurs in the time derivative and is due to the presence of a maximal monotone graph; the other comes up in the principal part of the PDE, where the p-Laplace operator is considered. The paper extends to the singular case 1 < p < 2, the results obtained previously by the second author for the degenerate case p > 2; it completes a regularity theory for a type of PDEs that model phase transitions for a material obeying a nonlinear law of diffusion. |
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On the Doubly Singular Equation γ(u)t = ∆_puDoubly singular PDEIntrinsic scalingPhase transitionRegularity theoryWe prove that local weak solutions of a nonlinear parabolic equation with a doubly singular character are locally continuous. One singularity occurs in the time derivative and is due to the presence of a maximal monotone graph; the other comes up in the principal part of the PDE, where the p-Laplace operator is considered. The paper extends to the singular case 1 < p < 2, the results obtained previously by the second author for the degenerate case p > 2; it completes a regularity theory for a type of PDEs that model phase transitions for a material obeying a nonlinear law of diffusion.Taylor & Francis2024-05-08T11:19:12Z2005-01-01T00:00:00Z2005info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10348/12448engDOI: 10.1081/PDE-200059308Henriques, Euricainfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-12T02:03:32Zoai:repositorio.utad.pt:10348/12448Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T16:35:53.333932Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse |
| dc.title.none.fl_str_mv |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| title |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| spellingShingle |
On the Doubly Singular Equation γ(u)t = ∆_pu Henriques, Eurica Doubly singular PDE Intrinsic scaling Phase transition Regularity theory |
| title_short |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| title_full |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| title_fullStr |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| title_full_unstemmed |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| title_sort |
On the Doubly Singular Equation γ(u)t = ∆_pu |
| author |
Henriques, Eurica |
| author_facet |
Henriques, Eurica |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Henriques, Eurica |
| dc.subject.por.fl_str_mv |
Doubly singular PDE Intrinsic scaling Phase transition Regularity theory |
| topic |
Doubly singular PDE Intrinsic scaling Phase transition Regularity theory |
| description |
We prove that local weak solutions of a nonlinear parabolic equation with a doubly singular character are locally continuous. One singularity occurs in the time derivative and is due to the presence of a maximal monotone graph; the other comes up in the principal part of the PDE, where the p-Laplace operator is considered. The paper extends to the singular case 1 < p < 2, the results obtained previously by the second author for the degenerate case p > 2; it completes a regularity theory for a type of PDEs that model phase transitions for a material obeying a nonlinear law of diffusion. |
| publishDate |
2005 |
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2005-01-01T00:00:00Z 2005 2024-05-08T11:19:12Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
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publishedVersion |
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https://hdl.handle.net/10348/12448 |
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https://hdl.handle.net/10348/12448 |
| dc.language.iso.fl_str_mv |
eng |
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eng |
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DOI: 10.1081/PDE-200059308 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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Taylor & Francis |
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Taylor & Francis |
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