The initial-boundary-value problem for the “good” Boussinesq equation on the half line
Studied here is an initial-boundary-value problem for the “good” Boussinesq equation on the half line. It is shown that this initial-boundary-value problem, when the initial-boundary-data satisfy certain compatible conditions, is well-posed in the L 2 -based Sobolev space H s ( R + ) for s > 1 2...
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| Veröffentlicht in: | Nonlinear analysis Jg. 69; H. 2; S. 647 - 682 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier Ltd
15.07.2008
Elsevier |
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| ISSN: | 0362-546X, 1873-5215 |
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| Abstract | Studied here is an initial-boundary-value problem for the “good” Boussinesq equation on the half line. It is shown that this initial-boundary-value problem, when the initial-boundary-data satisfy certain compatible conditions, is well-posed in the
L
2
-based Sobolev space
H
s
(
R
+
)
for
s
>
1
2
. In addition, the mapping that associated to appropriate initial-boundary-data the corresponding solution is analytic as a function between appropriate Banach spaces. |
|---|---|
| AbstractList | Studied here is an initial-boundary-value problem for the “good” Boussinesq equation on the half line. It is shown that this initial-boundary-value problem, when the initial-boundary-data satisfy certain compatible conditions, is well-posed in the
L
2
-based Sobolev space
H
s
(
R
+
)
for
s
>
1
2
. In addition, the mapping that associated to appropriate initial-boundary-data the corresponding solution is analytic as a function between appropriate Banach spaces. Studied here is an initial-boundary-value problem for the 'good' Boussinesq equation on the half line. It is shown that this initial-boundary-value problem, when the initial-boundary-data satisfy certain compatible conditions, is well-posed in the L2-based Sobolev space for . In addition, the mapping that associated to appropriate initial-boundary-data the corresponding solution is analytic as a function between appropriate Banach spaces. |
| Author | Xue, Ruying |
| Author_xml | – sequence: 1 givenname: Ruying surname: Xue fullname: Xue, Ruying email: ryxue@zju.edu.cn organization: Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China |
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| Cites_doi | 10.2206/kyushujm.59.443 10.1081/PDE-120016157 10.1080/03605300600718503 10.1007/PL00000962 10.4310/MAA.2000.v7.n1.a9 10.1090/S0002-9947-01-02885-9 10.1088/0951-7715/17/3/010 10.1006/jdeq.1993.1108 10.1063/1.530829 10.1016/j.jmaa.2005.04.041 10.1007/BF01218475 10.1016/S0362-546X(96)00093-4 |
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| Keywords | Initial-boundary-value problem 35G30 Boussinesq equation 35Q35 Existence Boundary value problem Initial value problem Nonlinear analysis Mathematical model |
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| References | Lototsky (b9) 2000; 7 Bona, Sachs (b3) 1988; 118 Holmer (b6) 2006; 31 Bona, Sun, Zheng (b4) 2001; 326 Saito (b12) 2005; 59 Bona, Chen, Saut (b2) 2004; 17 Pani, Saranga (b11) 1997; 29 Colliander, Kenig (b5) 2002; 27 Maligranda, Persson, Wyller (b10) 1994; 35 Varlamov (b13) 2000; 05 Lions, Magenes (b8) 1972 Alekseev, Smishliaev (b1) 2001; 3 Linares (b7) 1993; 106 Xue (b14) 2006; 316 Colliander (10.1016/j.na.2007.06.010_b5) 2002; 27 Varlamov (10.1016/j.na.2007.06.010_b13) 2000; 05 Bona (10.1016/j.na.2007.06.010_b4) 2001; 326 Bona (10.1016/j.na.2007.06.010_b3) 1988; 118 Maligranda (10.1016/j.na.2007.06.010_b10) 1994; 35 Pani (10.1016/j.na.2007.06.010_b11) 1997; 29 Bona (10.1016/j.na.2007.06.010_b2) 2004; 17 Holmer (10.1016/j.na.2007.06.010_b6) 2006; 31 Lions (10.1016/j.na.2007.06.010_b8) 1972 Linares (10.1016/j.na.2007.06.010_b7) 1993; 106 Lototsky (10.1016/j.na.2007.06.010_b9) 2000; 7 Xue (10.1016/j.na.2007.06.010_b14) 2006; 316 Alekseev (10.1016/j.na.2007.06.010_b1) 2001; 3 Saito (10.1016/j.na.2007.06.010_b12) 2005; 59 |
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| Snippet | Studied here is an initial-boundary-value problem for the “good” Boussinesq equation on the half line. It is shown that this initial-boundary-value problem,... Studied here is an initial-boundary-value problem for the 'good' Boussinesq equation on the half line. It is shown that this initial-boundary-value problem,... |
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| SubjectTerms | Boussinesq equation Exact sciences and technology Existence Initial-boundary-value problem Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use |
| Title | The initial-boundary-value problem for the “good” Boussinesq equation on the half line |
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