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Volumn 13, Issue 4, 2005, Pages 921-940

Comparison of quarter-plane and two-point boundary value problems: The BBM-equation

Author keywords

BBM equation; Comparison principles; Nonlinear dispersive wave equations; Quarter plane problems; Two point boundary value problems

Indexed keywords


EID: 28444465155     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.921     Document Type: Review
Times cited : (19)

References (29)
  • 2
    • 0003372381 scopus 로고
    • Lectures on nonlinear wave motion
    • (ed. A. Newell) American. Math. Soc.: Providence, RI
    • T.B. Benjamin, Lectures on nonlinear wave motion, In Lect. Appl. Math. Vol. 15, (ed. A. Newell) American. Math. Soc.: Providence, RI (1974), 3-47.
    • (1974) Lect. Appl. Math. , vol.15 , pp. 3-47
    • Benjamin, T.B.1
  • 4
    • 16744366059 scopus 로고
    • A mathematical model for long waves generated by wavemakers in nonlinear dispersive system
    • J.L. Bona and P.J. Bryant A mathematical model for long waves generated by wavemakers in nonlinear dispersive system, Proc. Cambridge Philos. Soc. 73 (1973) 391-405.
    • (1973) Proc. Cambridge Philos. Soc. , vol.73 , pp. 391-405
    • Bona, J.L.1    Bryant, P.J.2
  • 5
    • 0033229362 scopus 로고    scopus 로고
    • Comparison of model equations for small-amplitude long waves
    • J.L. Bona and H. Chen Comparison of model equations for small-amplitude long waves. Nonlinear Analysis TMA Series B, 38 (1999) 625-647.
    • (1999) Nonlinear Analysis TMA Series B , vol.38 , pp. 625-647
    • Bona, J.L.1    Chen, H.2
  • 6
    • 0000327541 scopus 로고    scopus 로고
    • A Boussinesq system for the two-way propagation of nonlinear dispersive waves
    • J.L. Bona and M. Chen A Boussinesq system for the two-way propagation of nonlinear dispersive waves, Physica D 116 (1998) 191-224.
    • (1998) Physica D , vol.116 , pp. 191-224
    • Bona, J.L.1    Chen, M.2
  • 7
    • 0011913755 scopus 로고    scopus 로고
    • Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
    • J.L. Bona, M. Chen and J.-C. Saut Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory, J. Nonlinear Sci. 12 (2002) 283-318.
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 283-318
    • Bona, J.L.1    Chen, M.2    Saut, J.-C.3
  • 8
    • 2442660478 scopus 로고    scopus 로고
    • Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media. II: Nonlinear theory
    • J.L. Bona, M. Chen and J.-C. Saut Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media. II: Nonlinear theory, Nonlinearity 17 (2004) 925-952.
    • (2004) Nonlinearity , vol.17 , pp. 925-952
    • Bona, J.L.1    Chen, M.2    Saut, J.-C.3
  • 9
    • 0001667814 scopus 로고
    • An initial and boundary value problem for a model equation for propagation of long waves
    • J.L. Bona and V. Dougalis An initial and boundary value problem for a model equation for propagation of long waves, J. Math. Anal. Appl. 75 (1980) 503-522.
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 503-522
    • Bona, J.L.1    Dougalis, V.2
  • 10
    • 0005182101 scopus 로고
    • Initial-boundary value problems for model equations for the propagation of long waves
    • Evolution Equations (ed. G. Gerreyra, G. Goldstein and F. Neubrander), Marcel Dekker: New York
    • J.L. Bona and L. Luo Initial-boundary value problems for model equations for the propagation of long waves. In Evolution Equations (ed. G. Gerreyra, G. Goldstein and F. Neubrander), Lecture Notes in Pure and Appl. Math., Marcel Dekker: New York, 168 (1995) 65-94.
    • (1995) Lecture Notes in Pure and Appl. Math. , vol.168 , pp. 65-94
    • Bona, J.L.1    Luo, L.2
  • 12
    • 0001610690 scopus 로고
    • Numerical schemes for a model for nonlinear dispersive waves
    • J.L. Bona, W.G. Pritchard and L.R. Scott Numerical schemes for a model for nonlinear dispersive waves, J. Comput. Phys. 60 (1985) 167-186.
    • (1985) J. Comput. Phys. , vol.60 , pp. 167-186
    • Bona, J.L.1    Pritchard, W.G.2    Scott, L.R.3
  • 13
    • 0141596147 scopus 로고    scopus 로고
    • A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain
    • J.L. Bona, S. Sun and B.-Y. Zhang, A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain, Comm. Partial Differential Equations 28 (2003) 1391-1436.
    • (2003) Comm. Partial Differential Equations , vol.28 , pp. 1391-1436
    • Bona, J.L.1    Sun, S.2    Zhang, B.-Y.3
  • 14
    • 28444468639 scopus 로고    scopus 로고
    • Wave generation by a moving boundary
    • J.L. Bona and V. Varlamov Wave generation by a moving boundary, Contemp. Math. 371 (2005) 41-71.
    • (2005) Contemp. Math. , vol.371 , pp. 41-71
    • Bona, J.L.1    Varlamov, V.2
  • 15
    • 0001681902 scopus 로고
    • Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire
    • J. Boussinesq Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire, C. R. Acad. Sci. Paris (1871) 72-73.
    • (1871) C. R. Acad. Sci. Paris , pp. 72-73
    • Boussinesq, J.1
  • 16
    • 0001864672 scopus 로고
    • Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenue dans ce canal des vitesses sensiblement pareilles de la surface au fond
    • J. Boussinesq Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenue dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appliq. Series II 17 (1872) 55-108.
    • (1872) J. Math. Pures Appliq. Series II , vol.17 , pp. 55-108
    • Boussinesq, J.1
  • 18
    • 0141672894 scopus 로고
    • Generalized boundary value problems for the Korteweg-de Vries equation in bounded domain
    • B.A. Bubnov Generalized boundary value problems for the Korteweg-de Vries equation in bounded domain, Diff. Eq. 15 (1979) 17-21.
    • (1979) Diff. Eq. , vol.15 , pp. 17-21
    • Bubnov, B.A.1
  • 19
    • 0012499847 scopus 로고    scopus 로고
    • An initial-boundary-value problem for the Korteweg-de Vries equation posed on a finite interval
    • T. Colin and J.-M. Ghidaglia An initial-boundary-value problem for the Korteweg-de Vries equation posed on a finite interval, Adv. Diff. Eq. 6 (2001) 1463-1492.
    • (2001) Adv. Diff. Eq. , vol.6 , pp. 1463-1492
    • Colin, T.1    Ghidaglia, J.-M.2
  • 20
    • 0035501532 scopus 로고    scopus 로고
    • An initial-boundary-value problem that approximates the quarter-plane problem for the Korteweg-de Vries equation
    • T. Colin and M. Gisclon An initial-boundary-value problem that approximates the quarter-plane problem for the Korteweg-de Vries equation, Nonlinear Anal. TMA, Series A 46 (2001) 869-892.
    • (2001) Nonlinear Anal. TMA, Series A , vol.46 , pp. 869-892
    • Colin, T.1    Gisclon, M.2
  • 21
    • 0034369460 scopus 로고    scopus 로고
    • Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval
    • B. Guo and J. Shen Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math. 86 (2000) 635-654.
    • (2000) Numer. Math. , vol.86 , pp. 635-654
    • Guo, B.1    Shen, J.2
  • 22
    • 84975987983 scopus 로고
    • A note on tsunamis: Their generation and propagation in an ocean of uniform depth
    • J. Hammack A note on tsunamis: their generation and propagation in an ocean of uniform depth, J. Fluid Mech. 60 (1973) 97-133.
    • (1973) J. Fluid Mech. , vol.60 , pp. 97-133
    • Hammack, J.1
  • 23
    • 0347907385 scopus 로고
    • The Korteweg-de Vries equation and water waves, part 2. Comparison with experiments
    • J. Hammack and H. Segur The Korteweg-de Vries equation and water waves, Part 2. Comparison with experiments, J. Fluid Mech. 65 (1974) 237-246.
    • (1974) J. Fluid Mech. , vol.65 , pp. 237-246
    • Hammack, J.1    Segur, H.2
  • 24
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves
    • D. J. Korteweg and G. de Vries On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Philosophical Magazine, 5th series, 36 (1895) 422-443.
    • (1895) Philosophical Magazine, 5th Series , vol.36 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 25
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: A survey of results
    • R. Miura The Korteweg-de Vries equation: a survey of results, SIAM Review 18 (1976) 412-459.
    • (1976) SIAM Review , vol.18 , pp. 412-459
    • Miura, R.1
  • 26
    • 84958426983 scopus 로고
    • Long waves on a beach
    • D.H. Peregrine, Long waves on a beach, J. Fluid Mechanics, 27 (1967) 815-827.
    • (1967) J. Fluid Mechanics , vol.27 , pp. 815-827
    • Peregrine, D.H.1
  • 27
    • 0000025473 scopus 로고
    • On the theory of oscillatory waves
    • G.G. Stokes, On the theory of oscillatory waves, Trans. Cambridge Philos. Soc. 8 (1847) 441-455.
    • (1847) Trans. Cambridge Philos. Soc. , vol.8 , pp. 441-455
    • Stokes, G.G.1
  • 29
    • 0042625574 scopus 로고
    • Analyticity of solutions for the generalized Korteweg-de Vries equation with respect to their initial datum
    • B.-Y. Zhang Analyticity of solutions for the generalized Korteweg-de Vries equation with respect to their initial datum, SIAM J. Math. Anal. 26 (1995) 1488-1513.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 1488-1513
    • Zhang, B.-Y.1


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