메뉴 건너뛰기




Volumn 38, Issue 4, 2006, Pages 1060-1074

On the semirelativistic Hartree-type equation

Author keywords

Global solution; Nonexistence of asymptotically free solutions; Scattering; Semirelativistic Hartree type equation

Indexed keywords

ASYMPTOTIC ANALYSIS; CONTROL NONLINEARITIES; PROBLEM SOLVING;

EID: 34249317023     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/060653688     Document Type: Article
Times cited : (103)

References (37)
  • 1
    • 0002598095 scopus 로고
    • n+1) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes
    • n+1) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes, Ann. Fac. Sci. Toulouse Math., 5 (1986/87), pp. 37-60.
    • (1986) Ann. Fac. Sci. Toulouse Math , vol.5 , pp. 37-60
    • BACHELOT, A.1
  • 2
    • 0001240303 scopus 로고
    • Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
    • J. E. BARAB, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., 25 (1984), pp. 3270-3274.
    • (1984) J. Math. Phys , vol.25 , pp. 3270-3274
    • BARAB, J.E.1
  • 4
    • 0000185785 scopus 로고
    • On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations
    • P. BRENNER, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, J. Differential Equations, 56 (1985), pp. 310-344.
    • (1985) J. Differential Equations , vol.56 , pp. 310-344
    • BRENNER, P.1
  • 5
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger Equations
    • New York University, Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI
    • T. CAZENAVE, Semilinear Schrödinger Equations, Courant Lecture Notes in Math. 10, New York University, Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI, 2003.
    • (2003) Courant Lecture Notes in Math , vol.10
    • CAZENAVE, T.1
  • 6
    • 33845538891 scopus 로고    scopus 로고
    • Remarks on modified improved Boussinesq equations in one space dimension
    • Y. CHO AND T. OZAWA, Remarks on modified improved Boussinesq equations in one space dimension, Proc. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 462 (2006), pp. 1949-1963.
    • (2006) Proc. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci , vol.462 , pp. 1949-1963
    • CHO, Y.1    OZAWA, T.2
  • 7
    • 0002645561 scopus 로고
    • Dispersion of small amplitude solution of the generalized Korteweg-de Vries equation
    • F. M. CHRIST AND M. I. WEINSTEIN, Dispersion of small amplitude solution of the generalized Korteweg-de Vries equation, J. Funct. Anal., 100 (1991), pp. 87-109.
    • (1991) J. Funct. Anal , vol.100 , pp. 87-109
    • CHRIST, F.M.1    WEINSTEIN, M.I.2
  • 8
    • 33847732573 scopus 로고    scopus 로고
    • Mean field dynamics of boson stars
    • to appear. Available online at
    • A. ELGART AND B. SCHLEIN, Mean field dynamics of boson stars, Comm. Pure Appl. Math., to appear. Available online at http://arxiv.org/abs/math-ph/0504051.
    • Comm. Pure Appl. Math
    • ELGART, A.1    SCHLEIN, B.2
  • 9
    • 34547160495 scopus 로고    scopus 로고
    • J. FRÖHLICH AND E. LENZMANN, Mean-field limit of quantum Bose gases and nonlinear Hartree equation, in Séminaire: Équations aux Dérivées Partielles., 2003-2004, Exp. No. xix, École Polytech., Pabsieu, 2004, pp. 1-26.
    • J. FRÖHLICH AND E. LENZMANN, Mean-field limit of quantum Bose gases and nonlinear Hartree equation, in Séminaire: Équations aux Dérivées Partielles., 2003-2004, Exp. No. xix, École Polytech., Pabsieu, 2004, pp. 1-26.
  • 10
    • 85056023191 scopus 로고    scopus 로고
    • Blow-up for nonlinear wave equations describing Boson stars
    • to appear. Available online at
    • J. FRÖHLICH AND E. LENZMANN, Blow-up for nonlinear wave equations describing Boson stars, Comm. Pure Appl. Math., to appear. Available online at http://arxiv.org/abs/math-ph/0511003.
    • Comm. Pure Appl. Math
    • FRÖHLICH, J.1    LENZMANN, E.2
  • 11
    • 0001632973 scopus 로고
    • Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2
    • J. GINIBRE AND T. OZAWA, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2, Comm. Math. Phys., 151 (1993), pp. 619-645.
    • (1993) Comm. Math. Phys , vol.151 , pp. 619-645
    • GINIBRE, J.1    OZAWA, T.2
  • 12
    • 0001522967 scopus 로고
    • On a class of nonlinear Schrödinger equations with nonlocal interaction
    • J. GINIBRE AND G. VELO, On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z., 170 (1980), pp. 109-136.
    • (1980) Math. Z , vol.170 , pp. 109-136
    • GINIBRE, J.1    VELO, G.2
  • 13
    • 0001270512 scopus 로고
    • Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations
    • J. GINIBRE AND G. VELO, Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor., 43 (1985), pp. 399-442.
    • (1985) Ann. Inst. H. Poincaré Phys. Théor , vol.43 , pp. 399-442
    • GINIBRE, J.1    VELO, G.2
  • 14
    • 0001547541 scopus 로고
    • On the asymptotic behavior of nonlinear wave equations
    • R. T. GLASSEY, On the asymptotic behavior of nonlinear wave equations, Trans. Amer. Math. Soc., 182 (1973), pp. 187-200.
    • (1973) Trans. Amer. Math. Soc , vol.182 , pp. 187-200
    • GLASSEY, R.T.1
  • 15
    • 0007327120 scopus 로고
    • Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations
    • R. T. GLASSEY, Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations, Comm. Math. Phys., 53 (1977), pp. 9-18.
    • (1977) Comm. Math. Phys , vol.53 , pp. 9-18
    • GLASSEY, R.T.1
  • 16
    • 38249025921 scopus 로고
    • Smoothing effect for some Schrödinger equations
    • N. HAYASHI AND T. OZAWA, Smoothing effect for some Schrödinger equations, J. Funct. Anal., 85 (1989), pp. 307-348.
    • (1989) J. Funct. Anal , vol.85 , pp. 307-348
    • HAYASHI, N.1    OZAWA, T.2
  • 19
    • 51649139542 scopus 로고
    • s-solutions and unconditional well-posedness
    • s-solutions and unconditional well-posedness, J. Anal. Math., 67 (1995), pp. 281-306.
    • (1995) J. Anal. Math , vol.67 , pp. 281-306
    • KATO, T.1
  • 20
    • 0000539356 scopus 로고
    • The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics
    • E. H. LIEB AND H.-T. YAU, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Comm. Math. Phys., 112 (1987), pp. 147-174.
    • (1987) Comm. Math. Phys , vol.112 , pp. 147-174
    • LIEB, E.H.1    YAU, H.-T.2
  • 22
    • 0036013587 scopus 로고    scopus 로고
    • Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations
    • S. MACHIHARA, K. NAKANISHI, AND T. OZAWA, Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations, Math. Ann., 322 (2002), pp. 603-621.
    • (2002) Math. Ann , vol.322 , pp. 603-621
    • MACHIHARA, S.1    NAKANISHI, K.2    OZAWA, T.3
  • 23
    • 0037570590 scopus 로고    scopus 로고
    • Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation
    • S. MACHIHARA, K. NAKANISHI, AND T. OZAWA, Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation, Rev. Mat. Iberoamericana, 19 (2003), pp. 179-194.
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 179-194
    • MACHIHARA, S.1    NAKANISHI, K.2    OZAWA, T.3
  • 24
    • 85024433210 scopus 로고
    • On the asymptotic behavior of solutions of semi-linear wave equations
    • A. MATSUMURA, On the asymptotic behavior of solutions of semi-linear wave equations, Publ. Res. Inst. Math. Sci., 12 (1976/77), pp. 169-189.
    • (1976) Publ. Res. Inst. Math. Sci , vol.12 , pp. 169-189
    • MATSUMURA, A.1
  • 25
    • 0141784178 scopus 로고
    • On a wave equation with a cubic convolution
    • G. P. MENZALA AND W. A. STRAUSS, On a wave equation with a cubic convolution, J. Differential Equations, 43 (1982), pp. 93-105.
    • (1982) J. Differential Equations , vol.43 , pp. 93-105
    • MENZALA, G.P.1    STRAUSS, W.A.2
  • 26
    • 0012711089 scopus 로고    scopus 로고
    • Modified wave operators for the Hartree equation with data, image and convergence in the same space
    • K. NAKANISHI, Modified wave operators for the Hartree equation with data, image and convergence in the same space, Comm. Pure Appl. Anal., 1 (2002), pp. 237-252.
    • (2002) Comm. Pure Appl. Anal , vol.1 , pp. 237-252
    • NAKANISHI, K.1
  • 27
    • 0036435214 scopus 로고    scopus 로고
    • Modified wave operators for the Hartree equation with data, image and convergence in the same space II
    • K. NAKANISHI, Modified wave operators for the Hartree equation with data, image and convergence in the same space II, Ann. Inst. H. Poincaré, 3 (2002), pp. 503-535.
    • (2002) Ann. Inst. H. Poincaré , vol.3 , pp. 503-535
    • NAKANISHI, K.1
  • 28
    • 0001178744 scopus 로고
    • Nonlinear scattering with nonlocal interaction
    • H. NAWA AND T. OZAWA, Nonlinear scattering with nonlocal interaction, Comm. Math. Phys., 146 (1992), pp. 259-275.
    • (1992) Comm. Math. Phys , vol.146 , pp. 259-275
    • NAWA, H.1    OZAWA, T.2
  • 29
    • 33644556142 scopus 로고    scopus 로고
    • Remarks on proofs of conservation laws for nonlinear Schrödinger equations
    • T. OZAWA, Remarks on proofs of conservation laws for nonlinear Schrödinger equations, Calc. Var. Partial Differential Equations, 25 (2006), pp. 403-408.
    • (2006) Calc. Var. Partial Differential Equations , vol.25 , pp. 403-408
    • OZAWA, T.1
  • 30
    • 0001284137 scopus 로고
    • Nonlinear small data scattering for the wave and Klein-Gordon equation
    • H. PECHER, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., 185 (1984), pp. 261-270.
    • (1984) Math. Z , vol.185 , pp. 261-270
    • PECHER, H.1
  • 31
    • 33750403756 scopus 로고    scopus 로고
    • Small data scattering for the Klein-Gordon equation with cubic convolution nonlinearity
    • H. SASAKI, Small data scattering for the Klein-Gordon equation with cubic convolution nonlinearity, Discrete Contin. Dynam. Systems, 15 (2006), pp. 973-981.
    • (2006) Discrete Contin. Dynam. Systems , vol.15 , pp. 973-981
    • SASAKI, H.1
  • 32
    • 0000617504 scopus 로고
    • Space-time decay for solutions of wave equations
    • I. SEGAL, Space-time decay for solutions of wave equations, Adv. in Math., 22 (1976), pp. 305-311.
    • (1976) Adv. in Math , vol.22 , pp. 305-311
    • SEGAL, I.1
  • 33
    • 0004136765 scopus 로고
    • Princeton University Press, Princeton, NJ
    • E. M. STEIN, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993.
    • (1993) Harmonic Analysis
    • STEIN, E.M.1
  • 34
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • W. A. STRAUSS, Nonlinear scattering theory at low energy, J. Funct. Anal., 41 (1981), pp. 110-133.
    • (1981) J. Funct. Anal , vol.41 , pp. 110-133
    • STRAUSS, W.A.1
  • 35
    • 0001684805 scopus 로고
    • Nonlinear scattering theory at low energy: Sequel
    • W. A. STRAUSS, Nonlinear scattering theory at low energy: Sequel, J. Funct. Anal., 43 (1981), pp. 281-293.
    • (1981) J. Funct. Anal , vol.43 , pp. 281-293
    • STRAUSS, W.A.1
  • 36
    • 0003353148 scopus 로고
    • Nonlinear Wave Equations, CBMS Reg
    • AMS, Providence, RI
    • W. A. STRAUSS, Nonlinear Wave Equations, CBMS Reg. Conf. Ser. Math. 73, AMS, Providence, RI, 1989.
    • (1989) Conf. Ser. Math , vol.73
    • STRAUSS, W.A.1
  • 37
    • 34547183678 scopus 로고    scopus 로고
    • Existence and blow up for a wave equation with a cubic convolution
    • World Scientific Publishing, River Edge, NJ
    • K. TSUTAYA, Existence and blow up for a wave equation with a cubic convolution, in Advances in Analysis, World Scientific Publishing, River Edge, NJ, 2005, pp. 321-325.
    • (2005) Advances in Analysis , pp. 321-325
    • TSUTAYA, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.