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Volumn 33, Issue 2, 2001, Pages 477-488

Global existence for systems of nonlinear wave equations in 3D with multiple speeds

Author keywords

Global existence; Null condition; Systems of nonlinear wave equations

Indexed keywords


EID: 0036050729     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141000378966     Document Type: Article
Times cited : (100)

References (21)
  • 3
    • 84990602498 scopus 로고
    • Global solutions of nonlinear hyperbolic equations for small initial data
    • D. CHRISTODOULOU, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math., 39 (1986), pp. 267-282.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 4
    • 0002046248 scopus 로고
    • The initial value problems for quasi-linear wave equations in two space dimensions with small data
    • A. HOSHIGA, The initial value problems for quasi-linear wave equations in two space dimensions with small data, Adv. Math. Sci. Appl., 5 (1995), pp. 67-89.
    • (1995) Adv. Math. Sci. Appl. , vol.5 , pp. 67-89
    • Hoshiga, A.1
  • 5
    • 0005422384 scopus 로고    scopus 로고
    • The lifespan of solutions to quasilinear hyperbolic systems in the critical case
    • A. HOSHIGA, The lifespan of solutions to quasilinear hyperbolic systems in the critical case, Funkcial. Ekvac., 41 (1998), pp. 167-188.
    • (1998) Funkcial. Ekvac. , vol.41 , pp. 167-188
    • Hoshiga, A.1
  • 6
    • 0034375234 scopus 로고    scopus 로고
    • Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition
    • A. HOSHIGA AND H. KUBO, Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition, SIAM J. Math. Anal., 31 (2000), pp. 486-513.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 486-513
    • Hoshiga, A.1    Kubo, H.2
  • 7
    • 84980140413 scopus 로고
    • Blow-up for quasilinear wave equations in three space dimensions
    • F. JOHN, Blow-up for quasilinear wave equations in three space dimensions, Comm. Pure Appl. Math. 34 (1981), pp. 29-51.
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 29-51
    • John, F.1
  • 8
    • 84990593419 scopus 로고
    • Almost global existence to nonlinear wave equations in three space dimensions
    • F. JOHN AND S. KLAINERMAN, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math., 37 (1984), pp. 443-455.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 443-455
    • John, F.1    Klainerman, S.2
  • 9
    • 84990555318 scopus 로고
    • Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data
    • F. JOHN, Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data, Comm. Pure Appl. Math., 40 (1987), pp. 79-109.
    • (1987) Comm. Pure Appl. Math. , vol.40 , pp. 79-109
    • John, F.1
  • 10
    • 0005512520 scopus 로고
    • Global existence for systems of nonlinear wave equations in two space dimensions
    • S. KATAYAMA, Global existence for systems of nonlinear wave equations in two space dimensions, Publ. Res. Inst. Math. Sci., 29 (1993), pp. 1021-1041.
    • (1993) Publ. Res. Inst. Math. Sci. , vol.29 , pp. 1021-1041
    • Katayama, S.1
  • 11
    • 84990619712 scopus 로고
    • Global, small amplitude solutions to nonlinear evolution equations
    • S. KLAINERMAN AND G. PONCE, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math., 36 (1983), pp. 133-141.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 133-141
    • Klainerman, S.1    Ponce, G.2
  • 12
    • 84990602599 scopus 로고
    • Uniform decay estimates and the Lorentz invariance of the classical wave equation
    • S. KLAINERMAN, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), pp. 321-332.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 321-332
    • Klainerman, S.1
  • 13
    • 0000870142 scopus 로고
    • The null condition and global existence to nonlinear wave equations
    • Nonlinear Systems of Partial Differential Equations in Applied Mathematics, AMS, Providence, RI
    • S. KLAINERMAN, The null condition and global existence to nonlinear wave equations, in Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1, Lectures in Appl. Math. 23, AMS, Providence, RI, 1986, pp. 293-326.
    • (1986) Lectures in Appl. Math. , vol.23 , Issue.1 PART , pp. 293-326
    • Klainerman, S.1
  • 15
    • 0030549709 scopus 로고    scopus 로고
    • On almost global existence for nonrelativistic wave equations in 3D
    • S. KLAINERMAN AND T. SIDERIS, On almost global existence for nonrelativistic wave equations in 3D, Comm. Pure Appl. Math., 49 (1996), pp. 307-321.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 307-321
    • Klainerman, S.1    Sideris, T.2
  • 16
    • 38249022216 scopus 로고
    • Resonance-type behaviour in a system of nonlinear wave equations
    • M. KOVALYOV, Resonance-type behaviour in a system of nonlinear wave equations, J. Differential Equations, 77 (1989), pp. 73-83.
    • (1989) J. Differential Equations , vol.77 , pp. 73-83
    • Kovalyov, M.1
  • 17
    • 0001152880 scopus 로고
    • Global existence of small solutions to nonlinear evolution equations
    • J. SHATAH, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations, 46 (1982), pp. 409-425.
    • (1982) J. Differential Equations , vol.46 , pp. 409-425
    • Shatah, J.1
  • 18
    • 84948321022 scopus 로고
    • Global behavior of solutions to nonlinear wave equations in three dimensions
    • T. SIDERIS, Global behavior of solutions to nonlinear wave equations in three dimensions, Comm. Partial Differential Equations, 8 (1983), pp. 1291-1323.
    • (1983) Comm. Partial Differential Equations , vol.8 , pp. 1291-1323
    • Sideris, T.1
  • 19
    • 0030532454 scopus 로고    scopus 로고
    • The null condition and global existence of nonlinear elastic waves
    • T. SIDERIS, The null condition and global existence of nonlinear elastic waves, Invent. Math., 123 (1996), pp. 323-342.
    • (1996) Invent. Math. , vol.123 , pp. 323-342
    • Sideris, T.1
  • 20
    • 0034399662 scopus 로고    scopus 로고
    • Nonresonance and global existence of prestressed nonlinear elastic waves
    • T. SIDERIS, Nonresonance and global existence of prestressed nonlinear elastic waves, Ann. of Math. (2), 151 (2000), pp. 849-874.
    • (2000) Ann. of Math. , vol.151 , Issue.2 , pp. 849-874
    • Sideris, T.1
  • 21
    • 0001321428 scopus 로고    scopus 로고
    • Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions
    • K. YOKOYAMA, Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions, J. Math. Soc. Japan, 52 (2000), pp. 609-632.
    • (2000) J. Math. Soc. Japan , vol.52 , pp. 609-632
    • Yokoyama, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.