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Volumn 26, Issue 1-2, 2001, Pages 205-232

Lifespan of solutions for two space dimensional wave equations with cubic nonlinearity

Author keywords

Lifespan; Nonlinear wave equations

Indexed keywords


EID: 13844300508     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100001753     Document Type: Article
Times cited : (18)

References (23)
  • 1
    • 0000870142 scopus 로고
    • The Null Condition and Global Existence to Nonlinear Wave Equations
    • Klainerman, S. The Null Condition and Global Existence to Nonlinear Wave Equations, Lect. Appl. Math. 1986, 23, 293-326.
    • (1986) Lect. Appl. Math. , vol.23 , pp. 293-326
    • Klainerman, S.1
  • 2
    • 84990602498 scopus 로고
    • Global Solutions of Nonlinear Hyperbolic Equations for Small Initial Data
    • Christodoulou, D. Global Solutions of Nonlinear Hyperbolic Equations for Small Initial Data. Comm. Pure Appl. Math. 1986, 39, 267-282.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 3
    • 1642305345 scopus 로고
    • Life-span of Classical Solutions to Nonlinear Wave Equations in Two Space Dimensions
    • Li, T.T.; Zhou, Y. Life-span of Classical Solutions to Nonlinear Wave Equations in Two Space Dimensions, J. Math. Pures Appl. 1994, 73, 223-249.
    • (1994) J. Math. Pures Appl. , vol.73 , pp. 223-249
    • Li, T.T.1    Zhou, Y.2
  • 4
    • 1642402713 scopus 로고
    • Life-span of Classical Solutions to Nonlinear Wave Equations in Two Space Dimensions II
    • Li, T.T.; Zhou, Y. Life-span of Classical Solutions to Nonlinear Wave Equations in Two Space Dimensions II, J. Partial Diff. Eqs. 1993, 6, 17-38.
    • (1993) J. Partial Diff. Eqs. , vol.6 , pp. 17-38
    • Li, T.T.1    Zhou, Y.2
  • 5
    • 84990619712 scopus 로고
    • Global, Small Amplitude Solutions to Nonlinear Evolution Equations
    • Klainerman, S.; Ponce, G. Global, Small Amplitude Solutions to Nonlinear Evolution Equations, Comm. Pure Appl. Math. 1983, 36, 133-141.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 133-141
    • Klainerman, S.1    Ponce, G.2
  • 6
    • 0001152880 scopus 로고
    • Global Existence of Small Solutions to Nonlinear Evolution Equations
    • Shatah, J. Global Existence of Small Solutions to Nonlinear Evolution Equations, J. Diff. Eq. 1982, 46, 409-425.
    • (1982) J. Diff. Eq. , vol.46 , pp. 409-425
    • Shatah, J.1
  • 7
    • 84990593419 scopus 로고
    • Almost Global Existence to General Nonlinear Wave Equations in Three Space-dimensions
    • John, F.; Klainerman, S. Almost Global Existence to General Nonlinear Wave Equations in Three Space-dimensions, Comm. Pure Appl. Math. 1984, 37, 235-268.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 235-268
    • John, F.1    Klainerman, S.2
  • 8
    • 84990602599 scopus 로고
    • Uniform Decay Estimates and the Lorentz Invariance of the Classical Wave Equation
    • Klainerman, S. Uniform Decay Estimates and the Lorentz Invariance of the Classical Wave Equation, Comm. Pure Appl. Math. 1985, 38, 321-332.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 321-332
    • Klainerman, S.1
  • 9
    • 84990555318 scopus 로고
    • Existence for Large Times of Strict Solutions of Nonlinear Wave Equations in Three Space Dimensions for Small Initial Data
    • John, F. Existence for Large Times of Strict Solutions of Nonlinear Wave Equations in Three Space Dimensions for Small Initial Data, Comm. Pure Appl. Math. 1987, 40, 79-109.
    • (1987) Comm. Pure Appl. Math. , vol.40 , pp. 79-109
    • John, F.1
  • 10
    • 84916159849 scopus 로고
    • Long-time Behavior of Solutions of a System of Nonlinear Wave Equations
    • Kovalyov, M. Long-time Behavior of Solutions of a System of Nonlinear Wave Equations, Commun. Partial Diff. Eq. 1987, 12, 471-501.
    • (1987) Commun. Partial Diff. Eq. , vol.12 , pp. 471-501
    • Kovalyov, M.1
  • 11
    • 0040537021 scopus 로고
    • Lifespan of Semilinear Wave Equations in Two Space Dimensions
    • Godin, P. Lifespan of Semilinear Wave Equations in Two Space Dimensions, Commun. Partial Diff. Eq. 1993, 18, 895-916.
    • (1993) Commun. Partial Diff. Eq. , vol.18 , pp. 895-916
    • Godin, P.1
  • 12
    • 0002046248 scopus 로고
    • The Initial Value Problems for Quasi-linear Wave Equations in Two Space Dimensions with Small Data
    • Hoshiga, A. The Initial Value Problems for Quasi-linear Wave Equations in Two Space Dimensions with Small Data, Adv. Math. Sci. Appl. 1995, 5, 67-89.
    • (1995) Adv. Math. Sci. Appl. , vol.5 , pp. 67-89
    • Hoshiga, A.1
  • 13
    • 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. 1990, 43, 445-472.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 445-472
    • Lindblad, H.1
  • 14
    • 13844304095 scopus 로고
    • Nonlinear Stability for Two Space Dimensional Wave Equations with Higher Order Perturbations
    • Li, T.T.; Zhou, Y. Nonlinear Stability for Two Space Dimensional Wave Equations with Higher Order Perturbations, Nonlin. World 1994, 1, 35-58.
    • (1994) Nonlin. World , vol.1 , pp. 35-58
    • Li, T.T.1    Zhou, Y.2
  • 17
    • 21544472219 scopus 로고    scopus 로고
    • Global Existence for Nonlinear Wave Equations in Two Space Dimensions
    • Gakuto International Ser., Math. Sci. Appl. Agemi, R., Giga, Y., Ozawa, T., Eds.; Gakkōtosho Co., Ltd.: Tokyo.
    • Katayama, S. Global Existence for Nonlinear Wave Equations in Two Space Dimensions. In Nonlinear Waves, Gakuto International Ser., Math. Sci. Appl. Agemi, R., Giga, Y., Ozawa, T., Eds.; Gakkōtosho Co., Ltd.: Tokyo. 1997, 10, 209-214.
    • (1997) Nonlinear Waves , vol.10 , pp. 209-214
    • Katayama, S.1
  • 18
    • 0000337016 scopus 로고
    • Existence in the Large for □u = F(u) in Two Space Dimensions
    • Glassey, R.T. Existence in the Large for □u = F(u) in Two Space Dimensions. Math. Z. 1981, 178, 233-261.
    • (1981) Math. Z. , vol.178 , pp. 233-261
    • Glassey, R.T.1
  • 20
    • 0011043137 scopus 로고
    • On Sobolev Spaces Associated with Some Lie Algebras
    • Ohya, Y., Kasahara, K., Shimakura, N., Kinokuniya: Tokyo
    • Hörmander, L. On Sobolev Spaces Associated with Some Lie Algebras. In Current Topics in Partial Differential Equations; Ohya, Y., Kasahara, K., Shimakura, N., Kinokuniya: Tokyo, 1986; 261-287.
    • (1986) Current Topics in Partial Differential Equations , pp. 261-287
    • Hörmander, L.1
  • 21
    • 0347384271 scopus 로고
    • ∞ Estimates for the Wave Operator
    • Contributions en l'Honneur de Lions, J.L.; Gauthier-Villars: Paris
    • ∞ Estimates for the Wave Operator. In Analyse Mathématique et Applications; Contributions en l'Honneur de Lions, J.L.; Gauthier-Villars: Paris, 1988; 211-234.
    • (1988) Analyse Mathématique et Applications , pp. 211-234
    • Hörmander, L.1
  • 22
    • 0040402801 scopus 로고
    • On the Fully Non-linear Cauchy Problem with Small Data. II
    • Microlocal Analysis and Nonlinear Waves, Beals, M., Melrose, R., Rauch, J., Springer-Verlag: New York
    • Hörmander, L. On the Fully Non-linear Cauchy Problem with Small Data. II. In Microlocal Analysis and Nonlinear Waves, IMA Vol. in Math and Its Applications; Beals, M., Melrose, R., Rauch, J., Springer-Verlag: New York, 1991; Vol. 30, 51-81.
    • (1991) IMA Vol. in Math and Its Applications , vol.30 , pp. 51-81
    • Hörmander, L.1
  • 23
    • 84980178173 scopus 로고
    • Global Existence for Nonlinear Wave Equations
    • Klainerman, S. Global Existence for Nonlinear Wave Equations, Comm. Pure Appl. Math. 1980, 33, 43-101.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 43-101
    • Klainerman, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.