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Volumn 233, Issue 1, 2000, Pages 75-91

On the blow-up rate and the blow-up set of breaking waves for a shallow water equation

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EID: 0034347295     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004793     Document Type: Article
Times cited : (318)

References (46)
  • 1
    • 0000310316 scopus 로고
    • The geometry of peaked solitons and billiard solutions of a class of integrable
    • Alber, M. S., Camassa, R., Holm, D., Marsden, J. E., The geometry of peaked solitons and billiard solutions of a class of integrable PDE's Letters Math. Phys. 32 (1994), 137-151.
    • (1994) PDE's Letters Math. Phys. , vol.32 , pp. 137-151
    • Alber, M.S.1    Camassa, R.2    Holm, D.3    Marsden, J.E.4
  • 2
    • 0000960226 scopus 로고
    • On the link between umbilic geodesies and soliton solutions of nonlinear
    • Alber, M. S., Camassa, R., Holm, D., Marsden, J. E., On the link between umbilic geodesies and soliton solutions of nonlinear PDE's Proc. Roy. Soc. London 450 (1995), 677-692.
    • (1995) PDE's Proc. Roy. Soc. London , vol.450 , pp. 677-692
    • Alber, M.S.1    Camassa, R.2    Holm, D.3    Marsden, J.E.4
  • 4
    • 0002074986 scopus 로고    scopus 로고
    • Blow-up of classical solutions of nonlinear hyperbolic equations: A survey of recent results
    • Birkhäuser, Boston
    • Alinhac, S., Blow-up of classical solutions of nonlinear hyperbolic equations: a survey of recent results, Progr. Nonlinear Differential Equations Appl., 21, Birkhäuser, Boston, (1996), 15-24.
    • (1996) Progr. Nonlinear Differential Equations Appl. , vol.21 , pp. 15-24
    • Alinhac, S.1
  • 6
    • 0001356905 scopus 로고
    • Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • Arnold, V., Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier 16 (1966), 319-361.
    • (1966) Ann. Inst. Fourier , vol.16 , pp. 319-361
    • Arnold, V.1
  • 7
    • 0009303159 scopus 로고
    • Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II
    • Bourgain, J., Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II, Geom. and Funct. Anal. 3 (1993), 209-262.
    • (1993) Geom. and Funct. Anal. , vol.3 , pp. 209-262
    • Bourgain, J.1
  • 8
    • 0000814560 scopus 로고    scopus 로고
    • Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation
    • Boyd, J. P., Peakons and coshoidal waves: traveling wave solutions of the Camassa-Holm equation, Appl. Math. Comput. 81 (1997), 173-187.
    • (1997) Appl. Math. Comput. , vol.81 , pp. 173-187
    • Boyd, J.P.1
  • 9
    • 0000495444 scopus 로고
    • An integrable Hamiltonian system
    • Calogero, F., An integrable Hamiltonian system, Phys. Letters A 201 (1995), 306-310.
    • (1995) Phys. Letters A , vol.201 , pp. 306-310
    • Calogero, F.1
  • 10
    • 0030546217 scopus 로고    scopus 로고
    • A completely integrable Hamiltonian system
    • Calogero, F. Francoise, J. P., A completely integrable Hamiltonian system, J. Math. Phys. 37 (1996), 2863-2871.
    • (1996) J. Math. Phys. , vol.37 , pp. 2863-2871
    • Calogero, F.1    Francoise, J.P.2
  • 11
    • 0030490914 scopus 로고    scopus 로고
    • Solvable quantum version of an integrable Hamiltonian system
    • Calogero, F. Vandiejen, J. F., Solvable quantum version of an integrable Hamiltonian system, J. Math. Phys. 37 (1996), 4243-4251.
    • (1996) J. Math. Phys. , vol.37 , pp. 4243-4251
    • Calogero, F.1    Vandiejen, J.F.2
  • 12
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa, R. 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
  • 13
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • Camassa, R., Holm, D. 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
  • 14
    • 0030970371 scopus 로고    scopus 로고
    • Symmetries of a class of nonlinear third-order partial differential equations
    • Clarkson, P., Mansfield, E. Priestley, T., Symmetries of a class of nonlinear third-order partial differential equations, Math. Comput. Modelling 25 (1997), 195-212.
    • (1997) Math. Comput. Modelling , vol.25 , pp. 195-212
    • Clarkson, P.1    Mansfield, E.2    Priestley, T.3
  • 15
    • 0000213450 scopus 로고    scopus 로고
    • On the Cauchy problem for the periodic Camassa-Holm equation
    • Constantin, A., On the Cauchy problem for the periodic Camassa-Holm equation, J. Differential Equations 141 (1997), 218-235.
    • (1997) J. Differential Equations , vol.141 , pp. 218-235
    • Constantin, A.1
  • 16
    • 0000684999 scopus 로고    scopus 로고
    • On the inverse spectral problem for the Camassa-Holm equation
    • Constantin, A., On the inverse spectral problem for the Camassa-Holm equation, J. Funct. Anal. 155 (1998), 352-363.
    • (1998) J. Funct. Anal. , vol.155 , pp. 352-363
    • Constantin, A.1
  • 17
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin, A. Escher, J., Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation, Comm. Pure Appl. Math. 51 (1998), 475-504.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 18
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • Constantin, A. 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
  • 19
    • 0000468550 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • Constantin, A. Escher, J., Global weak solutions for a shallow water equation, Indiana Univ. Math. J. 47 (1998), 1525-1545.
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 1525-1545
    • Constantin, A.1    Escher, J.2
  • 20
    • 0032328853 scopus 로고    scopus 로고
    • On the structure of a family of quasilinear equations arising in shallow water theory
    • Constantin, A. Escher, J., On the structure of a family of quasilinear equations arising in shallow water theory, Math. Ann. 312 (1998), 403-416.
    • (1998) Math. Ann. , vol.312 , pp. 403-416
    • Constantin, A.1    Escher, J.2
  • 21
  • 22
    • 0001662743 scopus 로고
    • Solitons in the Camassa-Holm shallow water equation
    • Cooper, F. Shepard. H., Solitons in the Camassa-Holm shallow water equation, Phys. Letters A 194 (1994), 246-250.
    • (1994) Phys. Letters A , vol.194 , pp. 246-250
    • Cooper, F.1    Shepard, H.2
  • 26
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the notion of an incompressible fluid
    • Ebin, D. Marsden, J. E., Groups of diffeomorphisms and the notion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163.
    • (1970) Ann. of Math. , vol.92 , pp. 102-163
    • Ebin, D.1    Marsden, J.E.2
  • 27
    • 0002080117 scopus 로고
    • Diffeomorphism groups, hydrodynamics and relativity and the notion of an incompressible fluid
    • (J. R. Vanstone, Ed.), Montreal
    • Ebin, D., Marsden, J. E., Fischer, A., Diffeomorphism groups, hydrodynamics and relativity and the notion of an incompressible fluid, Proc. 13th Biennal Seminar of Canad. Math. Congress (J. R. Vanstone, Ed.), Montreal (1972), 135-279.
    • (1972) Proc. 13th Biennal Seminar of Canad. Math. Congress , pp. 135-279
    • Ebin, D.1    Marsden, J.E.2    Fischer, A.3
  • 28
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformation and hereditary symmetries
    • Fokas, A. S. Fuchssteiner, B., Symplectic structures, their Bäcklund transformation and hereditary symmetries, Phys. D 4 1981/(1982), 47-66.
    • (1981) Phys. D , vol.4 , pp. 47-66
    • Fokas, A.S.1    Fuchssteiner, B.2
  • 29
    • 0001702502 scopus 로고
    • On a class of physically important integrable equations
    • Fokas, A. S., On a class of physically important integrable equations , Physica D 87 (1994), 145-150.
    • (1994) Physica D , vol.87 , pp. 145-150
    • Fokas, A.S.1
  • 30
    • 0002209413 scopus 로고    scopus 로고
    • A plethora of integrable bi-Hamiltonian equations
    • Ed. A. S. Fokas and I. M. Gelfand, Birkhäuser, Boston
    • Fokas, A. S., Olver, P. Rosenau, P., A plethora of integrable bi-Hamiltonian equations, Algebraic Aspects of Integrable Systems, Ed. A. S. Fokas and I. M. Gelfand, Birkhäuser, Boston (1997), 93-101.
    • (1997) Algebraic Aspects of Integrable Systems , pp. 93-101
    • Fokas, A.S.1    Olver, P.2    Rosenau, P.3
  • 31
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • Fuchssteiner, B., Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation, Phys. D 95 (1996), 229-243.
    • (1996) Phys. D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 32
    • 21844487106 scopus 로고
    • Factorization and Painléve analysis of a class of nonlinear third-order partial differential equations
    • Gilson, C. Pickering, A., Factorization and Painléve analysis of a class of nonlinear third-order partial differential equations, J. Phys. A 28 (1995), 2871-2888.
    • (1995) J. Phys. A , vol.28 , pp. 2871-2888
    • Gilson, C.1    Pickering, A.2
  • 33
    • 0001214956 scopus 로고    scopus 로고
    • Misiolek the Cauchy problem for a shallow water type equation
    • Himonas, A. G. Misiolek The Cauchy problem for a shallow water type equation, Comm. PDE 23 (1998), 123-139.
    • (1998) Comm. PDE , vol.23 , pp. 123-139
    • Himonas, A.G.1
  • 34
    • 0000376890 scopus 로고
    • The lifespan of classical solutions of nonlinear hyperbolic equations
    • Springer Verlag, Berlin-New York
    • Hörmander, L., The lifespan of classical solutions of nonlinear hyperbolic equations, Lecture Notes in Math., 1256, Springer Verlag, Berlin-New York, (1987), 214-280.
    • (1987) Lecture Notes in Math. , vol.1256 , pp. 214-280
    • Hörmander, L.1
  • 35
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • Kenig, C., Ponce, G. Vega, L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), 527-620.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 37
    • 0031535504 scopus 로고    scopus 로고
    • Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons
    • Li, Y. A. Olver, P., Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons, Discrete Contin. Dynam. Systems 3 (1997), 419-432.
    • (1997) Discrete Contin. Dynam. Systems , vol.3 , pp. 419-432
    • Li, Y.A.1    Olver, P.2
  • 38
    • 0031535504 scopus 로고    scopus 로고
    • Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Complex analytical behavior and convergence to non-analytic solutions
    • Li, Y. A. Olver, P., Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Complex analytical behavior and convergence to non-analytic solutions, Discrete Contin. Dynam. Systems 3 (1997), 419-432.
    • (1997) Discrete Contin. Dynam. Systems , vol.3 , pp. 419-432
    • Li, Y.A.1    Olver, P.2
  • 39
    • 0002497535 scopus 로고
    • Integrable systems and algebraic curves
    • Springer Verlag, New York
    • McKean, H. P., Integrable systems and algebraic curves, Lecture Notes in Math., 755, Springer Verlag, New York, (1979), 83-200.
    • (1979) Lecture Notes in Math. , vol.755 , pp. 83-200
    • McKean, H.P.1
  • 40
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation equation as a geodesic flow on the Bott-Virasoro group
    • Misiolek, G., A shallow water equation equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys. 24 (1998), 203-208.
    • (1998) J. Geom. Phys. , vol.24 , pp. 203-208
    • Misiolek, G.1
  • 42
    • 0030173112 scopus 로고    scopus 로고
    • Peakoms, R-matrix and toda lattice
    • Ragnisco, O. Bruschi, M., Peakoms, R-matrix and Toda lattice, Physica A 228 (1996), 150-159.
    • (1996) Physica A , vol.228 , pp. 150-159
    • Ragnisco, O.1    Bruschi, M.2
  • 43
    • 0030544208 scopus 로고    scopus 로고
    • Zero curvature formulations of dual hierarchies
    • Schiff, J., Zero curvature formulations of dual hierarchies, J. Math. Phys. 37 (1996), 1928-1938.
    • (1996) J. Math. Phys. , vol.37 , pp. 1928-1938
    • Schiff, J.1


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