NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR THE KORTEWEG-DE VRIES EQUATION ON A BOUNDED DOMAIN
This paper studies an initial-boundary-value problem （IBVP） of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space...
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| Published in | Journal of systems science and complexity Vol. 23; no. 3; pp. 499 - 526 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.06.2010
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1009-6124 1559-7067 |
| DOI | 10.1007/s11424-010-0143-x |
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| Abstract | This paper studies an initial-boundary-value problem （IBVP） of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space Hs（0, 1） for any s ≥ 0 via the contraction mapping Principle. |
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| AbstractList | This paper studies an initial-boundary-value problem （IBVP） of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space Hs（0, 1） for any s ≥ 0 via the contraction mapping Principle. This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space H s (0, 1) for any s ≥ 0 via the contraction mapping principle. |
| Author | Eugene F. KRAMER Bingyu ZHANG |
| AuthorAffiliation | Department of Mathematics, Physics, and Computer Science, University of Cincinnati, Raymond Walters College, Cincinnati, Ohio 45236, USA Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA |
| Author_xml | – sequence: 1 givenname: Eugene F. surname: Kramer fullname: Kramer, Eugene F. email: eugene.f.kramer@uc.edu organization: Department of Mathematics, Physics, and Computer Science, University of Cincinnati, Raymond Walters College – sequence: 2 givenname: Bingyu surname: Zhang fullname: Zhang, Bingyu organization: Department of Mathematical Sciences, University of Cincinnati |
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| CitedBy_id | crossref_primary_10_1051_cocv_2017001 crossref_primary_10_1007_s11424_018_6258_1 crossref_primary_10_1007_s12346_021_00472_y crossref_primary_10_1002_num_22590 crossref_primary_10_1016_j_jmaa_2016_06_063 crossref_primary_10_1137_15M103755X crossref_primary_10_1051_cocv_2012012 crossref_primary_10_1137_120891721 crossref_primary_10_1016_j_jmaa_2014_01_052 crossref_primary_10_11948_20180018 crossref_primary_10_1016_j_jde_2015_05_010 crossref_primary_10_1016_j_jmaa_2018_09_068 crossref_primary_10_3934_mcrf_2011_1_61 crossref_primary_10_1007_s40863_019_00120_z crossref_primary_10_1016_j_na_2022_113158 crossref_primary_10_1007_s10440_012_9676_4 crossref_primary_10_1134_S1995080221050048 |
| Cites_doi | 10.1007/BF01647967 10.1137/S0363012994269491 10.1098/rsta.1981.0178 10.1090/S0894-0347-03-00421-1 10.1070/SM1999v190n06ABEH000408 10.1090/S0894-0347-96-00200-7 10.1103/PhysRevLett.19.1095 10.1137/0331030 10.1006/jmaa.1995.1087 10.1016/0022-0396(88)90010-1 10.1098/rspa.1998.0178 10.1017/S0022112071001393 10.1002/cpa.3160460405 10.1090/S0002-9947-01-02885-9 10.1098/rsta.1975.0035 10.1137/S0036141093242600 10.1006/jfan.1995.1052 10.1137/0514085 10.1016/j.anihpc.2007.07.006 10.1081/PDE-120016157 10.1081/PDE-120024373 10.1016/0022-247X(70)90068-5 10.1007/BF02761431 10.1215/S0012-7094-89-05927-9 10.1007/BF01895688 10.1016/0022-0396(77)90046-8 10.1215/S0012-7094-76-04309-X 10.1103/PhysRevLett.68.3117 10.1007/s000290050008 10.1016/0378-4754(94)00021-2 10.1215/S0012-7094-06-13524-X 10.1017/S002211207400139X 10.1137/S0363012997327501 10.1006/jdeq.1994.1071 10.1017/S0022112073000479 10.1512/iumj.1991.40.40003 10.1080/03605300600718503 10.1215/S0012-7094-93-07101-3 10.1016/0960-0779(94)E0105-X 10.1002/cpa.3160210503 10.1137/1018076 10.1353/ajm.2003.0040 10.1081/PDE-200040191 10.1103/PhysRevLett.15.240 10.1007/BF01896020 10.57262/ade/1357139955 10.1090/S0894-0347-1988-0928265-0 10.1007/978-1-4612-5561-1 10.1007/978-1-4613-8460-1_9 10.1090/conm/221/03118 10.2172/4376203 10.1080/14786449508620739 10.1090/S0894-0347-1991-1086966-0 |
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| Keywords | Korteweg-de Vries equation KdV equation well-posed |
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| Notes | Q754 O175.8 11-4543/O1 KdV equation, Korteweg-de Vries equation, well-posed. |
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| Snippet | This paper studies an initial-boundary-value problem （IBVP） of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary... This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary... |
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| SubjectTerms | Complex Systems Control Mathematics Mathematics and Statistics Mathematics of Computing Operations Research/Decision Theory Statistics Systems Theory 初始边界值问题 压缩映射原理 德弗里斯 有界域 有限区间 线性问题 非齐次边界条件 |
| Title | NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR THE KORTEWEG-DE VRIES EQUATION ON A BOUNDED DOMAIN |
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