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Volumn 192, Issue 2, 2003, Pages 308-325

On global small amplitude solutions to systems of cubic nonlinear Klein-Gordon equations with different mass terms in one space dimension

Author keywords

Asymptotic behavior; Blow up; Nonlinear Klein Gordon equations; Small data global existence

Indexed keywords


EID: 0041656350     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00125-6     Document Type: Article
Times cited : (55)

References (23)
  • 2
    • 0039698677 scopus 로고    scopus 로고
    • Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace
    • J.-M. Delort, Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace, Ann. Inst. Henri Poincaré (Analyse non linéaire) 16 (1999) 563-591.
    • (1999) Ann. Inst. Henri Poincaré (Analyse Non Linéaire) , vol.16 , pp. 563-591
    • Delort, J.-M.1
  • 3
    • 0042238363 scopus 로고    scopus 로고
    • Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1
    • e Sér. 34 (2001) 1-61.
    • (2001) e Sér. , vol.34 , pp. 1-61
    • Delort, J.-M.1
  • 4
    • 51249175497 scopus 로고
    • Global solution of the system of wave and Klein-Gordon equations
    • V. Georgiev, Global solution of the system of wave and Klein-Gordon equations, Math. Z. 203 (1990) 683-698.
    • (1990) Math. Z. , vol.203 , pp. 683-698
    • Georgiev, V.1
  • 5
    • 0009297882 scopus 로고
    • Decay estimates for the Klein-Gordon equation
    • V. Georgiev, Decay estimates for the Klein-Gordon equation, Comm. Partial Differential Equations 17 (1992) 1111-1139.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 1111-1139
    • Georgiev, V.1
  • 6
    • 0042258739 scopus 로고    scopus 로고
    • Asymptotic behaviour of the one-dimensional Klein-Gordon equation with a cubic nonlinearity
    • preprint
    • V. Georgiev, B. Yordanov, Asymptotic behaviour of the one-dimensional Klein-Gordon equation with a cubic nonlinearity, preprint, 1996.
    • (1996)
    • Georgiev, V.1    Yordanov, B.2
  • 8
    • 0034375234 scopus 로고    scopus 로고
    • Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition
    • A. Hoshiga, H. Kubo, 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
  • 9
    • 84980140413 scopus 로고
    • Blow-up of solutions for quasi-linear wave equations in three space dimensions
    • F. John, Blow-up of solutions for quasi-linear 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
  • 10
    • 85008070309 scopus 로고
    • Global existence for systems of nonlinear wave equations in two dimensions, II
    • S. Katayama, Global existence for systems of nonlinear wave equations in two dimensions, II, Publ. RIMS 31 (1995) 645-665.
    • (1995) Publ. RIMS , vol.31 , pp. 645-665
    • Katayama, S.1
  • 11
    • 0033476185 scopus 로고    scopus 로고
    • A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension
    • S. Katayama, A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension, J. Math. Kyoto Univ. 39 (1999) 203-213.
    • (1999) J. Math. Kyoto Univ. , vol.39 , pp. 203-213
    • Katayama, S.1
  • 12
    • 0033148075 scopus 로고    scopus 로고
    • Small data blow-up for semilinear Klein-Gordon equations
    • M. Keel, T. Tao, Small data blow-up for semilinear Klein-Gordon equations, Amer. J. Math. 121 (1999) 629-669.
    • (1999) Amer. J. Math. , vol.121 , pp. 629-669
    • Keel, M.1    Tao, T.2
  • 13
    • 84990619688 scopus 로고
    • Global existence of small amplitude solutions to nonlinear Klein Gordon equations in four space-time dimensions
    • S. Klainerman, Global existence of small amplitude solutions to nonlinear Klein Gordon equations in four space-time dimensions, Comm. Pure. Appl. Math. 38 (1985) 631-641.
    • (1985) Comm. Pure. Appl. Math. , vol.38 , pp. 631-641
    • Klainerman, S.1
  • 14
    • 0000870142 scopus 로고
    • The null condition and global existence to nonlinear wave equations in three space dimensions
    • Amer. Math. Soc., Providence, RI
    • S. Klainerman, The null condition and global existence to nonlinear wave equations in three space dimensions, in: Lectures in Applied Mathematics, Vol. 23, Amer. Math. Soc., Providence, RI, 1986, pp. 293-326.
    • (1986) Lectures in Applied Mathematics , vol.23 , pp. 293-326
    • Klainerman, S.1
  • 15
    • 38249010090 scopus 로고
    • The unit condition and global existence for a class of nonlinear Klein-Gordon equations
    • R. Kosecki, The unit condition and global existence for a class of nonlinear Klein-Gordon equations, J. Differential Equations 100 (1992) 257-268.
    • (1992) J. Differential Equations , vol.100 , pp. 257-268
    • Kosecki, R.1
  • 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) 73-83.
    • (1989) J. Differential Equations , vol.77 , pp. 73-83
    • Kovalyov, M.1
  • 17
    • 0013004474 scopus 로고    scopus 로고
    • Small data blowup for systems of semilinear wave equations with different propagation speeds in three space dimensions
    • H. Kubo, M. Ohta, Small data blowup for systems of semilinear wave equations with different propagation speeds in three space dimensions, J. Differential Equations 163 (2000) 475-492.
    • (2000) J. Differential Equations , vol.163 , pp. 475-492
    • Kubo, H.1    Ohta, M.2
  • 18
    • 0039868840 scopus 로고    scopus 로고
    • Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension
    • K. Moriyama, Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension, Differential Integral Equations 10 (1997) 499-520.
    • (1997) Differential Integral Equations , vol.10 , pp. 499-520
    • Moriyama, K.1
  • 19
    • 0009232281 scopus 로고    scopus 로고
    • Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension
    • K. Moriyama, S. Tonegawa, Y. Tsutsumi, Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension, Funkcialaj Ekvacioj 40 (1997) 313-333.
    • (1997) Funkcialaj Ekvacioj , vol.40 , pp. 313-333
    • Moriyama, K.1    Tonegawa, S.2    Tsutsumi, Y.3
  • 20
    • 0001739203 scopus 로고    scopus 로고
    • Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions
    • T. Ozawa, K. Tsutaya, Y. Tsutsumi, Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions, Math. Z. 222 (1996) 341-362.
    • (1996) Math. Z. , vol.222 , pp. 341-362
    • Ozawa, T.1    Tsutaya, K.2    Tsutsumi, Y.3
  • 21
    • 84990623722 scopus 로고
    • Normal forms and quadratic nonlinear Klein-Gordon equations
    • J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure. Appl. Math. 38 (1985) 685-696.
    • (1985) Comm. Pure. Appl. Math. , vol.38 , pp. 685-696
    • Shatah, J.1
  • 22
    • 84964744325 scopus 로고    scopus 로고
    • Stability of constant equilibrium for the Maxwell-Higgs equations
    • Y. Tsutsumi, Stability of constant equilibrium for the Maxwell-Higgs equations, Funkcialaj Ekvacioj 46 (2003) 41-62.
    • (2003) Funkcialaj Ekvacioj , vol.46 , pp. 41-62
    • Tsutsumi, Y.1
  • 23
    • 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) 609-632.
    • (2000) J. Math. Soc. Japan , vol.52 , pp. 609-632
    • Yokoyama, K.1


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