메뉴 건너뛰기




Volumn 37, Issue 3, 2006, Pages 996-1026

Global solutions of the hunter - Saxton equation

Author keywords

Dissipative solution; Global conservative solutions; Nonlocal conservation law; Optimal transportation

Indexed keywords

DISSIPATIVE SOLUTION; GLOBAL CONSERVATIVE SOLUTIONS; NONLOCAL CONSERVATION LAW; OPTIMAL TRANSPORTATION;

EID: 33646540720     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/050623036     Document Type: Article
Times cited : (148)

References (27)
  • 2
    • 0012693456 scopus 로고    scopus 로고
    • Inverse scattering solutions of the Hunter - Saxton equation
    • [BSS]
    • [BSS] R. BEALS, D. SATTINGER, AND J. SZMIGIELSKI, Inverse scattering solutions of the Hunter - Saxton equation, Appl. Anal., 78 (2001), pp. 255-269.
    • (2001) Appl. Anal. , vol.78 , pp. 255-269
    • Beals, R.1    Sattinger, D.2    Szmigielski, J.3
  • 3
    • 0005706219 scopus 로고
    • Unique solutions for a class of discontinuous differential equations
    • [B]
    • [B] A. BRESSAN, Unique solutions for a class of discontinuous differential equations, Proc. Amer. Math. Soc., 104 (1988), pp. 772-778.
    • (1988) Proc. Amer. Math. Soc. , vol.104 , pp. 772-778
    • Bressan, A.1
  • 4
    • 30944454681 scopus 로고
    • Existence and continuous dependence for discontinuous O.D.E.'s
    • [BC]
    • [BC] A. BRESSAN AND G. COLOMBO, Existence and continuous dependence for discontinuous O.D.E.'s, Boll. Un. Mat. Ital. B (7), 4 (1990), pp. 295-311.
    • (1990) Boll. Un. Mat. Ital. B (7) , vol.4 , pp. 295-311
    • Bressan, A.1    Colombo, G.2
  • 5
    • 33646576045 scopus 로고    scopus 로고
    • An optimal transportation metric for solutions of the Camassa-Holm equation
    • [BF], to appear
    • [BF] A. BRESSAN AND M. FONTE, An optimal transportation metric for solutions of the Camassa-Holm equation, Math. Meth. Anal., to appear.
    • Math. Meth. Anal.
    • Bressan, A.1    Fonte, M.2
  • 8
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • [CH]
    • [CH] 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
  • 9
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • [C]
    • [C] A. CONSTANTIN, Existence of permanent and breaking waves for a shallow water equation: A geometric approach, Ann. Inst. Fourier (Grenoble), 50 (2000), pp. 321-362.
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , pp. 321-362
    • Constantin, A.1
  • 10
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • [CE]
    • [CE] 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
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • [CK]
    • [CK] A. CONSTANTIN AND B. KOLEV, Geodesic flow on the diffeomorphism group of the circle, Comment. Math. Helv., 78 (2003), pp. 787-804.
    • (2003) Comment. Math. Helv. , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 13
    • 0004456042 scopus 로고    scopus 로고
    • Transformations for the Camassa-Holm equation, its high-frequency limit and the Sinh - Gordon equation
    • [DP]
    • [DP] H. H. DAI AND M. PAVOLV, Transformations for the Camassa-Holm equation, its high-frequency limit and the Sinh - Gordon equation, J. Phys. Soc. Japan, 67 (1998), pp. 3655-3657.
    • (1998) J. Phys. Soc. Japan , vol.67 , pp. 3655-3657
    • Dai, H.H.1    Pavolv, M.2
  • 15
    • 0026390825 scopus 로고
    • Dynamics of director fields
    • [HS]
    • [HS] J. K. HUNTER AND R. SAXTON, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498-1521.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 1498-1521
    • Hunter, J.K.1    Saxton, R.2
  • 16
    • 0000452055 scopus 로고
    • On a completely integrable nonlinear hyperbolic variational equation
    • [HZ1]
    • [HZ1] J. K. HUNTER AND Y. ZHENG, On a completely integrable nonlinear hyperbolic variational equation, Phys. D, 79 (1994), pp. 361-386.
    • (1994) Phys. D , vol.79 , pp. 361-386
    • Hunter, J.K.1    Zheng, Y.2
  • 17
    • 34249761118 scopus 로고
    • On a nonlinear hyperbolic variational equation i
    • [HZ2]
    • [HZ2] J. K. HUNTER AND Y. ZHENG, On a nonlinear hyperbolic variational equation I, Arch. Rational Mech. Anal., 129 (1995), pp. 305-353.
    • (1995) Arch. Rational Mech. Anal. , vol.129 , pp. 305-353
    • Hunter, J.K.1    Zheng, Y.2
  • 18
    • 34249757026 scopus 로고
    • On a nonlinear hyperbolic variational equation II
    • [HZ3]
    • [HZ3] J. K. HUNTER AND Y. ZHENG, On a nonlinear hyperbolic variational equation II, Arch. Rational Mech. Anal., 129 (1995), pp. 355-383.
    • (1995) Arch. Rational Mech. Anal. , vol.129 , pp. 355-383
    • Hunter, J.K.1    Zheng, Y.2
  • 19
    • 0037171407 scopus 로고    scopus 로고
    • Camassa - Holm, Korteweg - De Vries and related models for water waves
    • [J]
    • [J] 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
  • 20
    • 0037612018 scopus 로고    scopus 로고
    • Euler equations on homogeneous spaces and Virasoro orbits
    • [KM]
    • [KM] B. KHESIN AND G. MISIOLEK, Euler equations on homogeneous spaces and Virasoro orbits, Adv. Math., 176 (2003), pp. 116-144.
    • (2003) Adv. Math. , vol.176 , pp. 116-144
    • Khesin, B.1    Misiolek, G.2
  • 21
    • 0033483085 scopus 로고    scopus 로고
    • The Camassa - Holm equation as a geodesic flow on the diffeomorphism group
    • [K]
    • [K] S. KOURANBAEVA, The Camassa - Holm equation as a geodesic flow on the diffeomorphism group, J. Math. Phys., 40 (1999), pp. 857-868.
    • (1999) J. Math. Phys. , vol.40 , pp. 857-868
    • Kouranbaeva, S.1
  • 25
    • 0012937773 scopus 로고    scopus 로고
    • On oscillations of an asymptotic equation of a nonlinear variational wave equation
    • [ZZ1]
    • [ZZ1] P. ZHANG AND Y. ZHENG, On oscillations of an asymptotic equation of a nonlinear variational wave equation, Asymptot. Anal., 18 (1998), pp. 307-327.
    • (1998) Asymptot. Anal. , vol.18 , pp. 307-327
    • Zhang, P.1    Zheng, Y.2
  • 26
    • 0000512953 scopus 로고    scopus 로고
    • On the existence and uniqueness of solutions to an asymptotic equation of a variational wave equation
    • [ZZ2]
    • [ZZ2] P. ZHANG AND Y. ZHENG, On the existence and uniqueness of solutions to an asymptotic equation of a variational wave equation, Acta Math. Sinica, 15 (1999), pp. 115-130.
    • (1999) Acta Math. Sinica , vol.15 , pp. 115-130
    • Zhang, P.1    Zheng, Y.2
  • 27
    • 0034359781 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data
    • [ZZ3]
    • [ZZ3] P. ZHANG AND Y. ZHENG, Existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data, Arch. Ration. Mech. Anal., 155 (2000), pp. 49-83.
    • (2000) Arch. Ration. Mech. Anal. , vol.155 , pp. 49-83
    • Zhang, P.1    Zheng, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.