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Volumn 33, Issue 3, 2004, Pages 607-636

The global existence theorem for quasi-linear wave equations with multiple speeds

Author keywords

Global existence; Non resonance; Quasi linear wave equations

Indexed keywords


EID: 33748521329     PISSN: 03854035     EISSN: None     Source Type: Journal    
DOI: 10.14492/hokmj/1285851913     Document Type: Article
Times cited : (16)

References (33)
  • 1
    • 0034348197 scopus 로고    scopus 로고
    • Global existence of nonlinear elastic waves
    • Agemi R., Global existence of nonlinear elastic waves, Invent. Math. 142 (2000), 225-250.
    • (2000) Invent. Math , vol.142 , pp. 225-250
    • Agemi, R.1
  • 3
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations
    • Bourgain J., Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations, Geom. Funct. Anal. 3 (1993), 107-156.
    • (1993) Geom. Funct. Anal , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 4
    • 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
  • 5
    • 84990602498 scopus 로고
    • Global solutions of nonlinear hyperbolic equations for small data
    • Christodoulou D., Global solutions of nonlinear hyperbolic equations for small data, Comm. Pure Appl. Math. 39 (1986), 267-282.
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 6
    • 0001762358 scopus 로고    scopus 로고
    • Small data scattering and blow-up for a wave equation with a cubic convolution
    • Hidano K., Small data scattering and blow-up for a wave equation with a cubic convolution, Funkcial. Ekvac. 43 (2000), 559-588.
    • (2000) Funkcial. Ekvac , vol.43 , pp. 559-588
    • Hidano, K.1
  • 7
    • 0035924632 scopus 로고    scopus 로고
    • Scattering problem for the nonlinear wave equation in the finite energy and conformai charge space
    • Hidano K., Scattering problem for the nonlinear wave equation in the finite energy and conformai charge space, J. Funct. Anal. 187 (2001), 274-307.
    • (2001) J. Funct. Anal , vol.187 , pp. 274-307
    • Hidano, K.1
  • 8
    • 3142700008 scopus 로고    scopus 로고
    • An elementary proof of global or almost global existence for quasi-linear wave equations
    • Hidano K., An elementary proof of global or almost global existence for quasi-linear wave equations, Tohoku Math. J. 56 (2) (2004), 271-287.
    • (2004) Tohoku Math. J , vol.56 , Issue.2 , pp. 271-287
    • Hidano, K.1
  • 10
    • 0034375234 scopus 로고    scopus 로고
    • Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition
    • Hoshiga A. and Kubo H., Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition, SIAM J. Math. Anal. 31 (2000), 486-513.
    • (2000) SIAM J. Math. Anal , vol.31 , pp. 486-513
    • Hoshiga, A.1    Kubo, H.2
  • 11
    • 59649129436 scopus 로고    scopus 로고
    • Global solvability for systems of nonlinear wave equations with multiple speeds in two space dimensions
    • Hoshiga A. and Kubo H., Global solvability for systems of nonlinear wave equations with multiple speeds in two space dimensions, Differential Integral Equations 17 (2004), 593-622.
    • (2004) Differential Integral Equations , vol.17 , pp. 593-622
    • Hoshiga, A.1    Kubo, H.2
  • 12
    • 84980140413 scopus 로고
    • Blow-up for quasilinear wave equations in three space dimensions
    • John F., Blow-up for quasilinear wave equations in three space dimensions, Comm. Pure Appl. Math. 34 (1981), 29-51.
    • (1981) Comm. Pure Appl. Math , vol.34 , pp. 29-51
    • John, F.1
  • 13
    • 84990553416 scopus 로고
    • Almost global existence of elastic waves of finite amplitude arising from small initial disturbances
    • John F., Almost global existence of elastic waves of finite amplitude arising from small initial disturbances, Comm. Pure Appl. Math. 41 (1988), 615-666.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 615-666
    • John, F.1
  • 15
    • 84990593419 scopus 로고
    • Almost global existence to nonlinear wave equations in three space dimensions
    • John F. and Klainerman S., Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37 (1984), 443-455.
    • (1984) Comm. Pure Appl. Math , vol.37 , pp. 443-455
    • John, F.1    Klainerman, S.2
  • 16
    • 85008070309 scopus 로고
    • Global existence for systems of nonlinear wave equations in two space dimensions. II
    • Katayama S., Global existence for systems of nonlinear wave equations in two space dimensions. II, Publ. Res. Inst. Math. Sci. 31 (1995), 645-665.
    • (1995) Publ. Res. Inst. Math. Sci , vol.31 , pp. 645-665
    • Katayama, S.1
  • 17
    • 0036436171 scopus 로고    scopus 로고
    • Almost global existence for some semilinear wave equations
    • Keel M., Smith F. and Sogge C.D., Almost global existence for some semilinear wave equations, J. Anal. Math. 87 (2002), 265-279.
    • (2002) J. Anal. Math , vol.87 , pp. 265-279
    • Keel, M.1    Smith, F.2    Sogge, C.D.3
  • 18
    • 0347659535 scopus 로고    scopus 로고
    • Almost global existence for quasilinear wave equations in three space dimensions
    • Keel M., Smith F. and Sogge C.D., Almost global existence for quasilinear wave equations in three space dimensions, J. Amer. Math. Soc. 17 (2004), 109-153.
    • (2004) J. Amer. Math. Soc , vol.17 , pp. 109-153
    • Keel, M.1    Smith, F.2    Sogge, C.D.3
  • 19
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equation
    • Kenig C.E., Ponce G. and Vega L., A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc. 9 (1996), 573-603.
    • (1996) J. Amer. Math. Soc , vol.9 , pp. 573-603
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 20
    • 84990602599 scopus 로고
    • Uniform decay estimate and the Lorentz invariance of the classical wave equations
    • Klainerman S., Uniform decay estimate and the Lorentz invariance of the classical wave equations, Comm. Pure Appl. Math. 38 (1985), 321-332.
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 321-332
    • Klainerman, S.1
  • 21
    • 0000870142 scopus 로고    scopus 로고
    • The null condition and global existence to nonlinear wave equations
    • (Santa Fe, NM, 1984), 293-326, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI
    • Klainerman S., The null condition and global existence to nonlinear wave equations, Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 (Santa Fe, NM, 1984), 293-326, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1996.
    • (1996) Nonlinear Systems of Partial Differential Equations in Applied Mathematics
    • Klainerman, S.1
  • 22
    • 84990556410 scopus 로고
    • Remarks on the global Sobolev inequalities in the Minkowski space R’l+1
    • Klainerman S., Remarks on the global Sobolev inequalities in the Minkowski space R’l+1, Comm. Pure Appl. Math. 40 (1987), 111-117.
    • (1987) Comm. Pure Appl. Math , vol.40 , pp. 111-117
    • Klainerman, S.1
  • 23
    • 0030549709 scopus 로고    scopus 로고
    • On almost global existence for nonrelativistic wave equations in 3D
    • Klainerman S. and Sideris T., On almost global existence for nonrelativistic wave equations in 3D, Comm. Pure Appl. Math. 49 (1996), 307-321.
    • (1996) Comm. Pure Appl. Math , vol.49 , pp. 307-321
    • Klainerman, S.1    Sideris, T.2
  • 24
    • 38249022216 scopus 로고
    • Resonance-type behaviour in a system of nonlinear wave equations
    • Kovalyov M., Resonance-type behaviour in a system of nonlinear wave equations, J. Diff. Eqns. 77 (1989), 73-83.
    • (1989) J. Diff. Eqns , vol.77 , pp. 73-83
    • Kovalyov, M.1
  • 25
    • 10944260665 scopus 로고    scopus 로고
    • Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation
    • Japan
    • Kubota K. and Yokoyama K., Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation, Japan. J. Math. (N.S.) 27 (2001), 113-202.
    • (2001) J. Math. (N.S.) , vol.27 , pp. 113-202
    • Kubota, K.1    Yokoyama, K.2
  • 26
    • 84990578237 scopus 로고
    • On the lifespan of solutions of nonlinear wave equations with small initial data
    • Lindblad H., On the lifespan of solutions of nonlinear wave equations with small initial data, Comm. Pure Appl. Math. 43 (1990), 445-472.
    • (1990) Comm. Pure Appl. Math , vol.43 , pp. 445-472
    • Lindblad, H.1
  • 27
    • 0033483674 scopus 로고    scopus 로고
    • Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions
    • Ozawa T., Tsutaya K. and Tsutsumi Y., Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions, Math. Ann. 313 (1999), 127-140.
    • (1999) Math. Ann , vol.313 , pp. 127-140
    • Ozawa, T.1    Tsutaya, K.2    Tsutsumi, Y.3
  • 28
    • 0030532454 scopus 로고    scopus 로고
    • The null condition and global existence of nonlinear elastic waves
    • Sideris T.C., The null condition and global existence of nonlinear elastic waves, Invent. Math. 123 (1996), 323-342.
    • (1996) Invent. Math , vol.123 , pp. 323-342
    • Sideris, T.C.1
  • 29
    • 0001376924 scopus 로고    scopus 로고
    • Delayed singularity formation in 2D compressible flow
    • Sideris T.C., Delayed singularity formation in 2D compressible flow, Amer. J. Math. 119 (1997), 371-422.
    • (1997) Amer. J. Math , vol.119 , pp. 371-422
    • Sideris, T.C.1
  • 30
    • 0034399662 scopus 로고    scopus 로고
    • Nonresonance and global existence of prestressed nonlinear elastic waves
    • Sideris T.C., Nonresonance and global existence of prestressed nonlinear elastic waves, Ann. Math. 151 (2) (2000), 849-874.
    • (2000) Ann. Math , vol.151 , Issue.2 , pp. 849-874
    • Sideris, T.C.1
  • 31
    • 0036050729 scopus 로고    scopus 로고
    • Global existence for systems of nonlinear wave equations in 3D with multiple speeds
    • Sideris T.C. and Tu S.-Y., Global existence for systems of nonlinear wave equations in 3D with multiple speeds, SIAM J. Math. Anal. 33 (2002), 477-488.
    • (2002) SIAM J. Math. Anal , vol.33 , pp. 477-488
    • Sideris, T.C.1    Tu, S.-Y.2
  • 32
    • 0346123238 scopus 로고    scopus 로고
    • Global existence for nonlinear wave equations with multiple speeds
    • Mount Holyoke (South Hadkey, MA), Contemp. Math., 320, Amer. Math. Soc., Providence, RI
    • Sogge C.D., Global existence for nonlinear wave equations with multiple speeds, Harmonic Analysis at Mount Holyoke (South Hadkey, MA, 2001), 353-366, Contemp. Math., 320, Amer. Math. Soc., Providence, RI, 2003.
    • (2001) Harmonic Analysis , pp. 353-366
    • Sogge, C.D.1
  • 33
    • 0001321428 scopus 로고    scopus 로고
    • Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions
    • Yokoyama K., Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions, J. Math. Soc. Japan 52 (2000), 609-632.
    • (2000) J. Math. Soc. Japan , vol.52 , pp. 609-632
    • Yokoyama, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.