메뉴 건너뛰기




Volumn 4, Issue 3, 2004, Pages 391-419

Well-posedness, global solutions and blowup phenomena for a nonlinearly dispersive wave equation

Author keywords

A nonlinearly dispersive wave equation; A sharp estimate of existence time; Blowup phenomena; Global solutions; Local well posedness

Indexed keywords


EID: 4444240304     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-004-0166-7     Document Type: Article
Times cited : (33)

References (34)
  • 2
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • BEALS, R., SATTINGER, D. and SZMIGIELSKI, J., Acoustic scattering and the extended Korteweg-de Vries hierarchy, Adv. Math. 140 (1998), 190-206.
    • (1998) Adv. Math. , vol.140 , pp. 190-206
    • Beals, R.1    Sattinger, D.2    Szmigielski, J.3
  • 4
    • 0001865962 scopus 로고
    • Model equations for long waves in nonlinear dispersive systems
    • London
    • BENJAMIN, T. B., BONA, J. L. and MAHONY, J. J., Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. (London) 272 (1972), 47-78.
    • (1972) Phil. Trans. R. Soc. , vol.272 , pp. 47-78
    • Benjamin, T.B.1    Bona, J.L.2    Mahony, J.J.3
  • 5
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • CAMASSA, R. and HOLM, D., An integrable shallow water equation with peaked solitons, Phys. Rev. Letters 71 (1993), 1661-1664.
    • (1993) Phys. Rev. Letters , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 6
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • CAMASSA, R., HOLM, D. and HYMAN, J., A new integrable shallow water equation, Adv. Appl. Mech. 31 (1994), 1-33.
    • (1994) Adv. Appl. Mech. , vol.31 , pp. 1-33
    • Camassa, R.1    Holm, D.2    Hyman, J.3
  • 7
    • 0002944990 scopus 로고    scopus 로고
    • The Hamiltonian structure of the Camassa-Holm equation
    • CONSTANTIN, A., The Hamiltonian structure of the Camassa-Holm equation. Exposition. Math. 15 (1997), 53-85.
    • (1997) Exposition. Math. , vol.15 , pp. 53-85
    • Constantin, A.1
  • 8
    • 0034415062 scopus 로고    scopus 로고
    • Global existence of solutions and breaking waves for a shallow water equation: A geometric approach
    • Grenoble
    • CONSTANTIN, A., Global existence of solutions and breaking waves for a shallow water equation: a geometric approach, Ann. Inst. Fourier (Grenoble) 50 (2000), 321-362.
    • (2000) Ann. Inst. Fourier , vol.50 , pp. 321-362
    • Constantin, A.1
  • 9
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the Camassa-Holm equation
    • CONSTANTIN, A., On the scattering problem for the Camassa-Holm equation, Proc. R. Soc. London A 457 (2001), 953-970.
    • (2001) Proc. R. Soc. London A , vol.457 , pp. 953-970
    • Constantin, A.1
  • 10
    • 85129402022 scopus 로고    scopus 로고
    • Global existence and blow-up for a shallow water equation
    • CONSTANTIN, A. and ESCHER, J., Global existence and blow-up for a shallow water equation, Annali Sc. Norm. Sup. Pisa 26 (1998), 303-328.
    • (1998) Annali Sc. Norm. Sup. Pisa , vol.26 , pp. 303-328
    • Constantin, A.1    Escher, J.2
  • 11
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • CONSTANTIN, A. and ESCHER, J., Wave breaking for nonlinear nonlocal shallow water equations, Acta Mathematica 181 (1998), 229-243.
    • (1998) Acta Mathematica , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 12
    • 0002231208 scopus 로고    scopus 로고
    • On the Cauchy problem for a family of quasilinear hyperbolic equations
    • CONSTANTIN, A. and ESCHER, J., On the Cauchy problem for a family of quasilinear hyperbolic equations, Comm. P.D.E. 23 (1998), 1449-1458.
    • (1998) Comm. P.D.E. , vol.23 , pp. 1449-1458
    • Constantin, A.1    Escher, J.2
  • 13
    • 0034347295 scopus 로고    scopus 로고
    • On the blow-up rate and the blow-up of breaking waves for a shallow water equation
    • CONSTANTIN, A. and ESCHER, J., On the blow-up rate and the blow-up of breaking waves for a shallow water equation, Math. Z. 233 (2000), 75-91.
    • (2000) Math. Z. , vol.233 , pp. 75-91
    • Constantin, A.1    Escher, J.2
  • 15
    • 0034729052 scopus 로고    scopus 로고
    • Stability of a class of solitary waves in compressible elastic rods
    • CONSTANTIN, A. and STRAUSS, W. A., Stability of a class of solitary waves in compressible elastic rods. Phys. Lett. A 270 (2000), 140-148.
    • (2000) Phys. Lett. A , vol.270 , pp. 140-148
    • Constantin, A.1    Strauss, W.A.2
  • 17
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • DAI, H. H., Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech. 127 (1998), 193-207.
    • (1998) Acta Mech. , vol.127 , pp. 193-207
    • Dai, H.H.1
  • 18
    • 0000171588 scopus 로고    scopus 로고
    • Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
    • DAI, H. H. and HUO, Y., Solitary shock waves and other travelling waves in a general compressible hyperelastic rod, Proc. R. Soc. London A 456 (2000), 331-363.
    • (2000) Proc. R. Soc. London A , vol.456 , pp. 331-363
    • Dai, H.H.1    Huo, Y.2
  • 19
    • 0000830886 scopus 로고    scopus 로고
    • A few remarks on the Camassa-Holm equation
    • DANCHIN, R., A few remarks on the Camassa-Holm equation. Differential and Integral Equations 14 (2001), 953-988.
    • (2001) Differential and Integral Equations , vol.14 , pp. 953-988
    • Danchin, R.1
  • 21
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformation and hereditary symmetries
    • FOKAS, A. and FUCHSSTEINER, B., Symplectic structures, their Bäcklund transformation and hereditary symmetries. Physica D 4 (1981), 47-66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fokas, A.1    Fuchssteiner, B.2
  • 22
    • 0002405102 scopus 로고    scopus 로고
    • The Cauchy problem for an integrable shallow water equation
    • HIMONAS, A. A. and MISIOLEK, G., The Cauchy problem for an integrable shallow water equation, Differential and Integral Equations 14 (2001), 821-831.
    • (2001) Differential and Integral Equations , vol.14 , pp. 821-831
    • Himonas, A.A.1    Misiolek, G.2
  • 23
    • 0037171407 scopus 로고    scopus 로고
    • Korteweg-de Vries and related models for water waves
    • JOHNSON, R. S., CAMASSA-HOLM, Korteweg-de Vries and related models for water waves, J. Fluid. Mech. 457 (2002), 63-82.
    • (2002) J. Fluid. Mech. , vol.457 , pp. 63-82
    • Johnson, R.S.1    Camassa-Holm2
  • 24
    • 1342300742 scopus 로고    scopus 로고
    • On solutions of the Camassa-Holm equation
    • JOHNSON, R. S., On solutions of the Camassa-Holm equation, Proc. R. Soc. London A, 459 (2003), 1687-1708.
    • (2003) Proc. R. Soc. London A , vol.459 , pp. 1687-1708
    • Johnson, R.S.1
  • 25
    • 0003123140 scopus 로고
    • Quasi-linear equations of evolution, with applications to partial differential equations
    • Spectral Theory and Differential Equations, Springer Verlag, Berlin
    • KATO, T., Quasi-linear equations of evolution, with applications to partial differential equations, in: Spectral Theory and Differential Equations, Lecture Notes in Math., Springer Verlag, Berlin, 448 (1975), 25-70.
    • (1975) Lecture Notes in Math. , vol.448 , pp. 25-70
    • Kato, T.1
  • 26
    • 0002362134 scopus 로고
    • On the Korteweg-de Vries equation
    • KATO, T., On the Korteweg-de Vries equation, Manuscripta Math. 28, (1979), 89-99.
    • (1979) Manuscripta Math. , vol.28 , pp. 89-99
    • Kato, T.1
  • 27
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (generalized) Korteweg-de Vries equation
    • Studies in Applied Mathematics, Academic Press, New York
    • KATO, T., On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in Applied Mathematics, Adv. Math. Suppl. Stud., Academic Press, New York, 8 (1983), 93-128.
    • (1983) Adv. Math. Suppl. Stud. , vol.8 , pp. 93-128
    • Kato, T.1
  • 28
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • KATO, T. and PONCE, G., Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), 891-907.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 29
    • 0034688728 scopus 로고    scopus 로고
    • Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
    • LI, Y. and OLVER, P., Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Differential Equations 162 (2000), 27-63.
    • (2000) J. Differential Equations , vol.162 , pp. 27-63
    • Li, Y.1    Olver, P.2
  • 31
    • 0035479874 scopus 로고    scopus 로고
    • On the Cauchy problem for the Camassa-Holm equation
    • RODRIGUEZ-BLANCO, G., On the Cauchy problem for the Camassa-Holm equation, Nonlinear Anal. 46 (2001), 309-327.
    • (2001) Nonlinear Anal. , vol.46 , pp. 309-327
    • Rodriguez-Blanco, G.1
  • 32
    • 84974399945 scopus 로고
    • Instability of a class of dispersive solitary waves
    • P. SOUGANIDIS and W. A. STRAUSS, Instability of a class of dispersive solitary waves, Proc. R. Soc. Edinburgh 114A (1990), 195-212
    • (1990) Proc. R. Soc. Edinburgh , vol.114 A , pp. 195-212
    • Souganidis, P.1    Strauss, W.A.2
  • 33
    • 0003353148 scopus 로고
    • Nonlinear Wave Equations
    • Amer. Math. Soc., Providence, R. I.
    • STRAUSS, W. A., Nonlinear Wave Equations, Conf. Board Math. Sci., vol. 73, Amer. Math. Soc., Providence, R. I., 1989.
    • (1989) Conf. Board Math. Sci. , vol.73
    • Strauss, W.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.