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Volumn 37, Issue 4, 2005, Pages 1044-1069

Global weak solutions to a generalized hyperelastic-rod wave equation

Author keywords

Camassa Holm equation; Existence; Hyperelastic rod wave equation; Uniqueness; Weak solutions

Indexed keywords

DATA ACQUISITION; DISPERSION (WAVES); MATHEMATICAL MODELS; NONLINEAR SYSTEMS; THEOREM PROVING;

EID: 33746133952     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/040616711     Document Type: Article
Times cited : (149)

References (36)
  • 1
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • R. SEALS, D. H. SATTINGER, AND J. SZMIGIELSKI, Acoustic scattering and the extended Korteweg-de Vries hierarchy, Adv. Math., 140 (1998), pp. 190-206.
    • (1998) Adv. Math. , vol.140 , pp. 190-206
    • Seals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 3
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • R. CAMASSA AND D. D. HOLM, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), pp. 1661-1664.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 5
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • A. CONSTANTIN, Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Ann. Inrt. Fourier (Grenoble), 50 (2000), pp. 321-362.
    • (2000) Ann. Inrt. Fourier (Grenoble) , vol.50 , pp. 321-362
    • Constantin, A.1
  • 8
    • 0000468550 scopus 로고
    • Global weak solutions for a shallow water equation
    • A. CONSTANTIN AND J. ESCHER, Global weak solutions for a shallow water equation, Indiana Univ. Math. J., 47 (1908), pp. 1527-1648.
    • (1908) Indiana Univ. Math. J. , vol.47 , pp. 1527-1648
    • Constantin, A.1    Escher, J.2
  • 9
    • 0002231208 scopus 로고    scopus 로고
    • On the Cauchy problem for a family of quasilinear hyperbolic equations
    • A. CONSTANTIN AND J. ESCHER, On the Cauchy problem for a family of quasilinear hyperbolic equations, Comm. Partial Differential Equations, 23 (1998), pp. 1449-1458.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 1449-1458
    • Constantin, A.1    Escher, J.2
  • 10
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • A. CONSTANTIN AND J. ESCHER, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math., 181 (1998), pp. 229-243.
    • (1998) Acta Math. , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 11
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • A. CONSTANTIN AND H. P. MCKEAN, A shallow water equation on the circle, Comm. Pure Appl. Math., 52 (1999), pp. 949-982.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 949-982
    • Constantin, A.1    Mckean, H.P.2
  • 12
    • 0034349440 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • A. CONSTANTIN AND L. MOLINET, Global weak solutions for a shallow water equation, Comm. Math. Phys., 211 (2000), pp. 45-61.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 45-61
    • Constantin, A.1    Molinet, L.2
  • 13
    • 0034729052 scopus 로고    scopus 로고
    • Stability of a class of solitary waves in compressible elastic rods
    • A. CONSTANTIN AND W. A. STRAUSS, Stability of a class of solitary waves in compressible elastic rods, Phys. Lett. A, 270 (2000), pp. 140-148.
    • (2000) Phys. Lett. A , vol.270 , pp. 140-148
    • Constantin, A.1    Strauss, W.A.2
  • 14
    • 0040599108 scopus 로고    scopus 로고
    • Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods
    • H.-H. DAI, Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods, Wave Motion, 28 (1998), pp. 367-381.
    • (1998) Wave Motion , vol.28 , pp. 367-381
    • Dai, H.-H.1
  • 15
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • H.-H. DAI, Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod, Acta Mech., 127 (1998), pp. 193-207.
    • (1998) Acta Mech. , vol.127 , pp. 193-207
    • Dai, H.-H.1
  • 16
    • 0000171588 scopus 로고    scopus 로고
    • Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
    • H.-H. DAI AND Y. HUO, Solitary shock waves and other travelling waves in a general compressible hyperelastic rod, R. Soc. Lond. Proc. Ser. A, Math. Phys. Eng. Sci., 456 (2000), pp. 331-363.
    • (2000) R. Soc. Lond. Proc. Ser. A, Math. Phys. Eng. Sci. , vol.456 , pp. 331-363
    • Dai, H.-H.1    Huo, Y.2
  • 17
    • 0000830886 scopus 로고    scopus 로고
    • A few remarks on the Camassa-Holm equation
    • R. DANCHIN, A few remarks on the Camassa-Holm equation, Differential Integral Equations, 14 (2001), pp. 953-988.
    • (2001) Differential Integral Equations , vol.14 , pp. 953-988
    • Danchin, R.1
  • 18
    • 0043159153 scopus 로고    scopus 로고
    • A note on well-posedness for Camassa-Holm equation
    • R. DANCHIN, A note on well-posedness for Camassa-Holm equation, J. Differential Equations, 192 (2003), pp. 429-444.
    • (2003) J. Differential Equations , vol.192 , pp. 429-444
    • Danchin, R.1
  • 19
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R. J. DIPERNA AND P.-L. LIONS, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), pp. 511-547.
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • Diperna, R.J.1    Lions, P.-L.2
  • 20
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • B. FUCHSSTEINER AND A. S. FOKAS, Symplectic structures, their Bäcklund transformations and hereditary symmetries, Phys. D, 4 (1981/82), pp. 47-66.
    • (1981) Phys. D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 21
    • 0002405102 scopus 로고    scopus 로고
    • The Cauchy problem for an integrable shallow-water equation
    • A. A. HIMONAS AND G. MISIOŁEK, The Cauchy problem for an integrable shallow-water equation, Differential Integral Equations, 14 (2001), pp. 821-831.
    • (2001) Differential Integral Equations , vol.14 , pp. 821-831
    • Himonas, A.A.1    Misiołek, G.2
  • 22
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • R. S. JOHNSON, Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech., 455 (2002), pp. 63-82.
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 23
    • 1042267877 scopus 로고    scopus 로고
    • Stability of solitary waves for a nonlinearly dispersive equation
    • H. KALISCH, Stability of solitary waves for a nonlinearly dispersive equation, Discrete Contin. Dyn. Syst., 10 (2004), pp. 709-717.
    • (2004) Discrete Contin. Dyn. Syst. , vol.10 , pp. 709-717
    • Kalisch, H.1
  • 24
    • 0034688728 scopus 로고    scopus 로고
    • Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
    • Y. A. LI AND P. J. OLVER, Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Differential Equations, 162 (2000), pp. 27-63.
    • (2000) J. Differential Equations , vol.162 , pp. 27-63
    • Li, Y.A.1    Olver, P.J.2
  • 25
    • 0242648945 scopus 로고    scopus 로고
    • Analysis
    • 2nd ed., American Mathematical Society, Providence, RI
    • E. H. LIEB AND M. LOSS, Analysis, Graduate Studies In Mathematics 14, 2nd ed., American Mathematical Society, Providence, RI, 2001.
    • (2001) Graduate Studies in Mathematics , vol.14
    • Lieb, E.H.1    Loss, M.2
  • 26
    • 0003280262 scopus 로고
    • Mathematical topics in fluid mechanics, vol. 1. Incompressible modela
    • Oxford University Press, New York
    • P.-L. LIONS, Mathematical Topics in Fluid Mechanics, Vol. 1. Incompressible Modela, in Oxford Lecture Series in Mathematics and its Applications, 3, Oxford University Press, New York, 1906.
    • (1906) Oxford Lecture Series in Mathematics and Its Applications , vol.3
    • Lions, P.-L.1
  • 27
    • 0040421182 scopus 로고    scopus 로고
    • Mathematical topics in fluid mechanics, vol 2. Compressible models
    • Oxford University Press, New York
    • P.-L. LIONS, Mathematical Topics in Fluid Mechanics, Vol 2. Compressible Models, in Oxford Lecture Series in Mathematics and its Applications, 10, Oxford University Press, New York, 1998.
    • (1998) Oxford Lecture Series in Mathematics and Its Applications , vol.10
    • Lions, P.-L.1
  • 28
    • 2942657000 scopus 로고    scopus 로고
    • Stability of peakons for the generalized Camassa-Holm equation
    • electronic
    • O. LOPES, Stability of peakons for the generalized Camassa-Holm equation, Electron. J. Differential Equations, (electronic), 2003.
    • (2003) Electron. J. Differential Equations
    • Lopes, O.1
  • 29
    • 0034825095 scopus 로고    scopus 로고
    • Peakons and periodic cusp waves in a generalized Camassa-Holm equation
    • T. QIAN AND M. TANG, Peakons and periodic cusp waves in a generalized Camassa-Holm equation, Cheat Solitons Fractals, 12 (2001), pp. 1347-1360.
    • (2001) Cheat Solitons Fractals , vol.12 , pp. 1347-1360
    • Qian, T.1    Tang, M.2
  • 30
    • 0035479874 scopus 로고    scopus 로고
    • On the Cauchy problem for the Camasta-Holm equation
    • O. RODRÍGUEZ-BLANCO, On the Cauchy problem for the Camasta-Holm equation, Nonlinear Anal., 46 (2001), pp. 309-327.
    • (2001) Nonlinear Anal. , vol.46 , pp. 309-327
    • Rodríguez-Blanco, O.1
  • 32
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solutions to a shallow water equation
    • Z. XIN AND P. ZHANG, On the weak solutions to a shallow water equation, Comm. Pure Appl. Math., 53 (2000), pp. 1411-1433.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2
  • 33
    • 0036913863 scopus 로고    scopus 로고
    • On the uniqueness and large time behavior of the weak solutions to a shallow water aquation
    • Z. XIN AND P. ZHANG, On the uniqueness and large time behavior of the weak solutions to a shallow water aquation, Comm. Partial Differential Equations, 27 (2002), pp. 1815-1844.
    • (2002) Comm. Partial Differential Equations , vol.27 , pp. 1815-1844
    • Xin, Z.1    Zhang, P.2
  • 34
    • 2942650679 scopus 로고    scopus 로고
    • On the blow-up scenario for the generalized Camassa-Holm equation
    • Z. YIN, On the blow-up scenario for the generalized Camassa-Holm equation, Comm. Partial Differential Equations, 29 (2004), pp. 867-877.
    • (2004) Comm. Partial Differential Equations , vol.29 , pp. 867-877
    • Yin, Z.1
  • 35
    • 33746128201 scopus 로고    scopus 로고
    • On the Cauchy problem for the generalised Camassa-Holm equation
    • to appear
    • Z. YIN, On the Cauchy problem for the generalised Camassa-Holm equation, Nonlinear Anal., to appear.
    • Nonlinear Anal.
    • Yin, Z.1
  • 36
    • 0037281017 scopus 로고    scopus 로고
    • On the Cauchy problem for a nonlinearly dispersive wave equation
    • Z. YIN, On the Cauchy problem for a nonlinearly dispersive wave equation, J. Nonlinear Math. Phys., 10 (2003), pp. 10-16.
    • (2003) J. Nonlinear Math. Phys. , vol.10 , pp. 10-16
    • Yin, Z.1


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