CAUCHY PROBLEM FOR A DEGENERATE PARABOLIC EQUATION WITH NON-DIVERGENCE FORM
In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form.
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| Published in | Acta mathematica scientia Vol. 30; no. 5; pp. 1679 - 1686 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2010
Department of Mathematics,Dalian Nationalities University,Dalian 116600,China%Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(10)60161-0 |
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| Abstract | In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. |
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| AbstractList | O1; In this article,it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. |
| Author | 周文书 姚正安 |
| AuthorAffiliation | Department of Mathematics, Dalian Nationalities University, Dalian 116600, China Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China |
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| Cites_doi | 10.1090/S0273-0979-1992-00266-5 10.1016/S0252-9602(07)60008-3 10.1090/pspum/065/1662747 10.1017/S0956792500002497 |
| ClassificationCodes | O1 |
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| Copyright | 2010 Wuhan Institute of Physics and Mathematics Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| DOI | 10.1016/S0252-9602(10)60161-0 |
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| Keywords | degenerate parabolic equation viscosity solution uniqueness existence 35K57 35K55 35K65 |
| Language | English |
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| Notes | degenerate parabolic equation viscosity solution degenerate parabolic equation; viscosity solution; uniqueness; existence uniqueness existence 42-1227/O O175.27 O175.26 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| References | Ladyzenskaja, Solonnikov, Ural'ceva (bib4) 1968 Hulshof, Vazquez (bib3) 1996; 7 Mu, Hu, Li, Cui (bib6) 2007; 27B Caffarelli, Vazquez (bib1) 1999; 65 Wu, Zhao, Yin, Li (bib5) 2001 Crandall, Ishii, Lions (bib2) 1992; 27 Caffarelli (10.1016/S0252-9602(10)60161-0_bib1) 1999; 65 Wu (10.1016/S0252-9602(10)60161-0_bib5) 2001 Crandall (10.1016/S0252-9602(10)60161-0_bib2) 1992; 27 Mu (10.1016/S0252-9602(10)60161-0_bib6) 2007; 27B Ladyzenskaja (10.1016/S0252-9602(10)60161-0_bib4) 1968 Hulshof (10.1016/S0252-9602(10)60161-0_bib3) 1996; 7 |
| References_xml | – volume: 7 start-page: 453 year: 1996 end-page: 471 ident: bib3 article-title: Maximal viscosity solutions of the modified porous medium equation and their asymptotic behavior publication-title: European J Appl Math – year: 2001 ident: bib5 publication-title: Nonlinear Diffusion Equations – volume: 27B start-page: 92 year: 2007 end-page: 106 ident: bib6 article-title: Blow-up and global existence for a coupled system of degenerate parabolic equations in a bounded domain publication-title: Acta Mathematica Scientia – volume: 27 start-page: 1 year: 1992 end-page: 67 ident: bib2 article-title: User's guide to viscosity solutions of second order partial differential equations publication-title: Bull Amer Math Soc – volume: 65 start-page: 13 year: 1999 end-page: 26 ident: bib1 article-title: Viscosity solutions for the porous medium equation publication-title: Proceeding of Symposia in Pure Mathematics – year: 1968 ident: bib4 publication-title: Linear and Quasilinear Equations of Parabolic Type. Transl Math Mono Vol 23 – volume: 27 start-page: 1 issue: 1 year: 1992 ident: 10.1016/S0252-9602(10)60161-0_bib2 article-title: User's guide to viscosity solutions of second order partial differential equations publication-title: Bull Amer Math Soc doi: 10.1090/S0273-0979-1992-00266-5 – volume: 27B start-page: 92 issue: 1 year: 2007 ident: 10.1016/S0252-9602(10)60161-0_bib6 article-title: Blow-up and global existence for a coupled system of degenerate parabolic equations in a bounded domain publication-title: Acta Mathematica Scientia doi: 10.1016/S0252-9602(07)60008-3 – volume: 65 start-page: 13 year: 1999 ident: 10.1016/S0252-9602(10)60161-0_bib1 article-title: Viscosity solutions for the porous medium equation publication-title: Proceeding of Symposia in Pure Mathematics doi: 10.1090/pspum/065/1662747 – year: 1968 ident: 10.1016/S0252-9602(10)60161-0_bib4 – year: 2001 ident: 10.1016/S0252-9602(10)60161-0_bib5 – volume: 7 start-page: 453 year: 1996 ident: 10.1016/S0252-9602(10)60161-0_bib3 article-title: Maximal viscosity solutions of the modified porous medium equation and their asymptotic behavior publication-title: European J Appl Math doi: 10.1017/S0956792500002497 |
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| Snippet | In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. O1; In this article,it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence... |
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| SubjectTerms | 35K55 35K57 35K65 Cauchy problem Cauchy问题 degenerate parabolic equation existence Mathematical analysis uniqueness Viscosity viscosity solution 抛物方程 柯西问题 退化抛物型方程 非散度型 |
| Title | CAUCHY PROBLEM FOR A DEGENERATE PARABOLIC EQUATION WITH NON-DIVERGENCE FORM |
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