메뉴 건너뛰기




Volumn 250, Issue 1, 2007, Pages 227-248

Blow-up of solutions to the DGH equation

Author keywords

Best constant; Convolution problem; Integrable equation; Singularity

Indexed keywords


EID: 34547117359     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.04.019     Document Type: Article
Times cited : (71)

References (40)
  • 1
    • 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
  • 3
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II: The KdV equation
    • Bourgain J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II: The KdV equation. Geom. Funct. Anal. 3 (1993) 209-262
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 209-262
    • Bourgain, J.1
  • 4
    • 33846878957 scopus 로고    scopus 로고
    • Global conservative solutions of the Camassa-Holm equation
    • Bressan A., and Constantin A. Global conservative solutions of the Camassa-Holm equation. Arch. Ration. Mech. Anal. 183 (2007) 215-239
    • (2007) Arch. Ration. Mech. Anal. , vol.183 , pp. 215-239
    • Bressan, A.1    Constantin, A.2
  • 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. Lett. 71 (1993) 1661-1664
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 6
    • 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
  • 7
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • Constantin A. Existence of permanent and breaking waves for a shallow water equation: A geometric approach. Ann. Inst. Fourier (Grenoble) 50 2 (2000) 321-362
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , Issue.2 , pp. 321-362
    • Constantin, A.1
  • 8
    • 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. Roy. Soc. London Ser. A 457 (2001) 953-970
    • (2001) Proc. Roy. Soc. London Ser. A , vol.457 , pp. 953-970
    • Constantin, A.1
  • 9
    • 17044434265 scopus 로고    scopus 로고
    • Finite propagation speed for the Camassa-Holm equation
    • 023506, 4 pp
    • Constantin A. Finite propagation speed for the Camassa-Holm equation. J. Math. Phys. 46 (2005) 023506, 4 pp
    • (2005) J. Math. Phys. , vol.46
    • Constantin, A.1
  • 10
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence and blow-up phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin A., and Escher J. Well-posedness, global existence and blow-up 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
  • 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 Math. 181 (1998) 229-243
    • (1998) Acta Math. , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 12
    • 0034347295 scopus 로고    scopus 로고
    • On the blow-up rate and blow-up set of breaking waves for a shallow water equation
    • Constantin A., and Escher J. On the blow-up rate and blow-up set 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
  • 13
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • Constantin A., and Kolev B. On the geometric approach to the motion of inertial mechanical systems. J. Phys. A 35 32 (2002) R51-R79
    • (2002) J. Phys. A , vol.35 , Issue.32
    • Constantin, A.1    Kolev, B.2
  • 14
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin A., and Kolev B. Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78 4 (2003) 787-804
    • (2003) Comment. Math. Helv. , vol.78 , Issue.4 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 15
  • 16
    • 0034349440 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • Constantin A., and Molinet L. Global weak solutions for a shallow water equation. Comm. Math. Phys. 211 1 (2000) 45-61
    • (2000) Comm. Math. Phys. , vol.211 , Issue.1 , pp. 45-61
    • Constantin, A.1    Molinet, L.2
  • 18
    • 0000380413 scopus 로고    scopus 로고
    • Stability of the Camassa-Holm solitons
    • Constantin A., and Strauss W. Stability of the Camassa-Holm solitons. J. Nonlinear Sci. 12 (2002) 415-422
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 415-422
    • Constantin, A.1    Strauss, W.2
  • 19
    • 33846053142 scopus 로고    scopus 로고
    • Inverse scattering transform for the Camassa-Holm equation
    • Constantin A., Gerdjikov V., and Ivanov R. Inverse scattering transform for the Camassa-Holm equation. Inverse Problems 22 (2006) 2197-2207
    • (2006) Inverse Problems , vol.22 , pp. 2197-2207
    • Constantin, A.1    Gerdjikov, V.2    Ivanov, R.3
  • 21
    • 40749103220 scopus 로고    scopus 로고
    • An integrable shallow water equation with linear and nonlinear dispersion
    • Dullin H., Gottwald G., and Holm D. An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett. 87 (2001) 1945-1948
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 1945-1948
    • Dullin, H.1    Gottwald, G.2    Holm, D.3
  • 22
    • 33847632920 scopus 로고    scopus 로고
    • Persistence properties and unique continuation of solutions of the Camassa-Holm equation
    • Himonas A., Misiołek G., Ponce G., and Zhou Y. Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Comm. Math. Phys. 271 (2007) 511-522
    • (2007) Comm. Math. Phys. , vol.271 , pp. 511-522
    • Himonas, A.1    Misiołek, G.2    Ponce, G.3    Zhou, Y.4
  • 23
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, 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. 455 (2002) 63-82
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 24
    • 0003123140 scopus 로고
    • Quasi-linear equations of evolution, with applications to partial differential equations
    • Spectral Theory and Differential Equations, Proc. Sympos. dedicated to Konrad Jorgens. Dundee, 1974, Springer, Berlin
    • Kato T. Quasi-linear equations of evolution, with applications to partial differential equations. Spectral Theory and Differential Equations, Proc. Sympos. dedicated to Konrad Jorgens. Dundee, 1974. Lecture Notes in Math. vol. 448 (1975), Springer, Berlin 25-70
    • (1975) Lecture Notes in Math. , vol.448 , pp. 25-70
    • Kato, T.1
  • 25
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • Kenig C., Ponce G., and 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
  • 26
    • 0034688728 scopus 로고    scopus 로고
    • Well-posedness and blow-up solutions for an integrable nonlinear dispersive model wave equation
    • Li Y., and Olver P. Well-posedness and blow-up solutions for an integrable nonlinear 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
  • 27
    • 33744819468 scopus 로고    scopus 로고
    • Global existence and blow-up solutions for a nonlinear shallow water equation
    • Liu Y. Global existence and blow-up solutions for a nonlinear shallow water equation. Math. Ann. 335 3 (2006) 717-735
    • (2006) Math. Ann. , vol.335 , Issue.3 , pp. 717-735
    • Liu, Y.1
  • 28
    • 0001472433 scopus 로고    scopus 로고
    • Breakdown of a shallow water equation
    • McKean H.P. Breakdown of a shallow water equation. Asian J. Math. 2 4 (1998) 867-874
    • (1998) Asian J. Math. , vol.2 , Issue.4 , pp. 867-874
    • McKean, H.P.1
  • 29
    • 0036436154 scopus 로고    scopus 로고
    • Classical solutions of the periodic Camassa-Holm equation
    • Misiołek G. Classical solutions of the periodic Camassa-Holm equation. Geom. Funct. Anal. 12 5 (2002) 1080-1104
    • (2002) Geom. Funct. Anal. , vol.12 , Issue.5 , pp. 1080-1104
    • Misiołek, G.1
  • 30
    • 10044263161 scopus 로고    scopus 로고
    • On well-posedness results for Camassa-Holm equation on the line: A survey
    • Molinet L. On well-posedness results for Camassa-Holm equation on the line: A survey. J. Nonlin. Math. Phys. 11 4 (2004) 521-533
    • (2004) J. Nonlin. Math. Phys. , vol.11 , Issue.4 , pp. 521-533
    • Molinet, L.1
  • 31
    • 0037906126 scopus 로고
    • A note on the breaking of waves
    • Seliger R. A note on the breaking of waves. Proc. Roy. Soc. London Ser. A 303 (1968) 493-496
    • (1968) Proc. Roy. Soc. London Ser. A , vol.303 , pp. 493-496
    • Seliger, R.1
  • 32
    • 0002936313 scopus 로고    scopus 로고
    • 1 metric and mean hydrodynamics
    • 1 metric and mean hydrodynamics. J. Funct. Anal. 160 1 (1998) 337-365
    • (1998) J. Funct. Anal. , vol.160 , Issue.1 , pp. 337-365
    • Shkoller, S.1
  • 33
    • 84859630809 scopus 로고    scopus 로고
    • Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
    • Springer-Verlag, Berlin
    • Struwe M. Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. Ergeb. Math. Grenzgeb. (3). second ed. vol. 34 (1996), Springer-Verlag, Berlin
    • (1996) Ergeb. Math. Grenzgeb. (3). second ed. , vol.34
    • Struwe, M.1
  • 34
    • 33748572115 scopus 로고    scopus 로고
    • Low-regularity global solutions to nonlinear dispersive equations
    • Surveys in Analysis and Operator Theory. Canberra, 2001, Austral. Nat. Univ., Canberra
    • Tao T. Low-regularity global solutions to nonlinear dispersive equations. Surveys in Analysis and Operator Theory. Canberra, 2001. Proc. Centre Math. Appl. Austral. Nat. Univ. vol. 40 (2002), Austral. Nat. Univ., Canberra 19-48
    • (2002) Proc. Centre Math. Appl. Austral. Nat. Univ. , vol.40 , pp. 19-48
    • Tao, T.1
  • 35
    • 21344447273 scopus 로고    scopus 로고
    • On the Cauchy problem and the scattering problem for the Dullin-Gottwald-Holm equation
    • Tian L., Gui G., and Liu Y. On the Cauchy problem and the scattering problem for the Dullin-Gottwald-Holm equation. Comm. Math. Phys. 257 3 (2005) 667-701
    • (2005) Comm. Math. Phys. , vol.257 , Issue.3 , pp. 667-701
    • Tian, L.1    Gui, G.2    Liu, Y.3
  • 36
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solution to a shallow water equation
    • Xin Z., and Zhang P. On the weak solution to a shallow water equation. Comm. Pure Appl. Math. 53 (2000) 1411-1433
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2
  • 37
    • 11944265069 scopus 로고    scopus 로고
    • Global existence and blow-up for a periodic integrable shallow water equation with linear and nonlinear dispersion
    • Yin Z. Global existence and blow-up for a periodic integrable shallow water equation with linear and nonlinear dispersion. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 12 1 (2005) 87-101
    • (2005) Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. , vol.12 , Issue.1 , pp. 87-101
    • Yin, Z.1
  • 38
    • 1342306310 scopus 로고    scopus 로고
    • Wave breaking for a periodic shallow water equation
    • Zhou Y. Wave breaking for a periodic shallow water equation. J. Math. Anal. Appl. 290 (2004) 591-604
    • (2004) J. Math. Anal. Appl. , vol.290 , pp. 591-604
    • Zhou, Y.1
  • 39
    • 2042468818 scopus 로고    scopus 로고
    • Wave breaking for a shallow water equation
    • Zhou Y. Wave breaking for a shallow water equation. Nonlinear Anal. 57 1 (2004) 137-152
    • (2004) Nonlinear Anal. , vol.57 , Issue.1 , pp. 137-152
    • Zhou, Y.1
  • 40
    • 30344445708 scopus 로고    scopus 로고
    • Blow-up of solutions to a nonlinear dispersive rod equation
    • Zhou Y. Blow-up of solutions to a nonlinear dispersive rod equation. Calc. Var. Partial Differential Equations 25 1 (2006) 63-77
    • (2006) Calc. Var. Partial Differential Equations , vol.25 , Issue.1 , pp. 63-77
    • Zhou, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.