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Volumn 3, Issue 1, 1996, Pages 77-91

Dispersive smoothing for Schrödinger equations

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EID: 0030497126     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1996.v3.n1.a8     Document Type: Article
Times cited : (23)

References (45)
  • 1
    • 0003369859 scopus 로고
    • Propagation des singularités des solutions d'équations analogues à l'équa-tion de Schrödinger
    • Springer-Verlag, Berlin-Heidelberg-New York
    • [BdeM] L. Boutet de Monvel, Propagation des singularités des solutions d'équations analogues à l'équa-tion de Schrödinger, Fourier Integral Operators and Partial Differential Equations, (Lecture Notes in Math., No. 459), Springer-Verlag, Berlin-Heidelberg-New York, 1975.
    • (1975) Fourier Integral Operators and Partial Differential Equations, Lecture Notes in Math. , vol.459
    • Boutet De Monvel, L.1
  • 4
    • 84972551383 scopus 로고
    • The Cauchy problem for Schrödinger type equations with variable coefficients
    • [I 1] W. Ichinose, The Cauchy problem for Schrödinger type equations with variable coefficients, Osaka J. Math. 24 (1987), 853-886.
    • (1987) Osaka J. Math. , vol.24 , pp. 853-886
    • Ichinose, W.1
  • 5
    • 84972566457 scopus 로고
    • 2 well posedness of the Cauchy problem for Schrödinger type equations on the Riemannian manifold and the Maslov theory
    • 2 well posedness of the Cauchy problem for Schrödinger type equations on the Riemannian manifold and the Maslov theory, Duke Math. J. 56 (1988), no. 3, 549-588.
    • (1988) Duke Math. J. , vol.56 , Issue.3 , pp. 549-588
  • 6
    • 0011495867 scopus 로고
    • Local decay in time of solutions to Schrödinger's equation witha dilation-analytic interaction
    • [J 1] A. Jensen, Local decay in time of solutions to Schrödinger's equation witha dilation-analytic interaction, Manuscripta Math. 25 (1978), 61-77.
    • (1978) Manuscripta Math. , vol.25 , pp. 61-77
    • Jensen, A.1
  • 7
    • 84972562665 scopus 로고
    • m), m ≥ 5
    • 4):, J. Math. Anal. Appl. 101 (1984), 397-422.
    • (1980) Duke Math. J. , vol.47 , pp. 57-80
  • 8
    • 84972562665 scopus 로고
    • 4)
    • 4):, J. Math. Anal. Appl. 101 (1984), 397-422.
    • (1984) J. Math. Anal. Appl. , vol.101 , pp. 397-422
  • 9
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • [JK] A. Jensen and T, Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. Journal 46 (1979), 583-611.
    • (1979) Duke Math. Journal , vol.46 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 11
    • 0000175040 scopus 로고
    • On a construction of the fundamental solution for Schrödinger equations
    • [Ki 1] H. Kitada, On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci. Univ. Tokyo IA 27 (1980), 193-226.
    • (1980) J. Fac. Sci. Univ. Tokyo IA , vol.27 , pp. 193-226
    • Kitada, H.1
  • 12
    • 0011512844 scopus 로고
    • Fundamental solutions and eigenfunction expansions for Schrödinger operators: I. Fundamental solutions
    • [Ki 2] _, Fundamental Solutions and eigenfunction expansions for Schrödinger operators: I. Fundamental solutions, Math. Z. 198 (1988), 181-190.
    • (1988) Math. Z. , vol.198 , pp. 181-190
  • 14
    • 84980086000 scopus 로고
    • Exponential decay of solutions of the wave equation in exterior of a star-shaped obstacle
    • [LMP] P. D. Lax, C. S. Morawetz, and R. S. Phillips, Exponential decay of solutions of the wave equation in exterior of a star-shaped obstacle, Comm. Pure Appl. Math. 16 (1963), 477-486.
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 477-486
    • Lax, P.D.1    Morawetz, C.S.2    Phillips, R.S.3
  • 16
    • 84972554366 scopus 로고
    • Singularities and energy decay in acoustical scattering
    • [Me] R. B. Melrose, Singularities and energy decay in acoustical scattering, Duke Math. J. 46 (1979), no. 1, 43-59.
    • (1979) Duke Math. J. , vol.46 , Issue.1 , pp. 43-59
    • Melrose, R.B.1
  • 17
    • 84980157470 scopus 로고
    • Singularities of boundary problems, I
    • [MS] R. B. Melrose and J. Sjostrand, Singularities of boundary problems, I, Comm. Pure Appl. Math. 31 (1978), 593-617; II, Comm. Pure Appl. Math. 35 (1982), 129-168.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 593-617
    • Melrose, R.B.1    Sjostrand, J.2
  • 18
    • 84980143702 scopus 로고
    • II
    • [MS] R. B. Melrose and J. Sjostrand, Singularities of boundary problems, I, Comm. Pure Appl. Math. 31 (1978), 593-617; II, Comm. Pure Appl. Math. 35 (1982), 129-168.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 129-168
  • 20
    • 84980087895 scopus 로고
    • The decay of solutions of the exterior initial-boundary value problem for the wave equation
    • [Mo 1] C. S. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961), 561-568.
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 561-568
    • Morawetz, C.S.1
  • 21
    • 84980086658 scopus 로고
    • The limiting amplitude principle
    • [Mo 2] _, The limiting amplitude principle, Comm. Pure Appl. Math. 15 (1962), 349-361.
    • (1962) Comm. Pure Appl. Math. , vol.15 , pp. 349-361
  • 22
    • 84981754014 scopus 로고
    • Exponential decay of solutions of the wave equation
    • [Mo 3] _, Exponential decay of solutions of the wave equation, Comm. Pure Appl. Math. 19 (1966), 439-444.
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 439-444
  • 23
    • 0000408939 scopus 로고
    • Time decay for the nonlinear Klein-Gordon equation
    • [Mo 4] _, Time decay for the nonlinear Klein-Gordon equation, Proc. Roy. Soc. A. 306 (1968), 291-296.
    • (1968) Proc. Roy. Soc. A. , vol.306 , pp. 291-296
  • 24
    • 84980131041 scopus 로고
    • Decay for solutions of the exterior problem for the wave equation
    • [Mo 5] _, Decay for solutions of the exterior problem for the wave equation, Comm. Pure Appl. Math. 28 (1975), 229-264.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 229-264
  • 25
    • 84980140132 scopus 로고
    • Decay of solutions of the wave equation outside nontrapping obstacles
    • [MRS] C. S. Morawetz, J. V. Ralston, and W. Strauss, Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math. 30 (1977), 447-508.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 447-508
    • Morawetz, C.S.1    Ralston, J.V.2    Strauss, W.3
  • 26
    • 85008270823 scopus 로고
    • Rate of decay of local energy and spectral properties of elliptic operators
    • [Mu] M. Murata, Rate of decay of local energy and spectral properties of elliptic operators, Japan J. Math. 60 (1980), 77-127.
    • (1980) Japan J. Math. , vol.60 , pp. 77-127
    • Murata, M.1
  • 27
    • 36749118628 scopus 로고
    • The evolution kernels: Uniform asymptotics expansions
    • [OF] T. A. Osborn and Y. Fujiwara, The evolution kernels: uniform asymptotics expansions, J. Math. Phys. 24 (1983), no. 5, 1093-1103.
    • (1983) J. Math. Phys. , vol.24 , Issue.5 , pp. 1093-1103
    • Osborn, T.A.1    Fujiwara, Y.2
  • 29
    • 84981752412 scopus 로고
    • Solutions of the wave equation with localized energy
    • [Ral 1] J. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math. 22 (1969), 807-823.
    • (1969) Comm. Pure Appl. Math. , vol.22 , pp. 807-823
    • Ralston, J.1
  • 30
    • 84972554073 scopus 로고
    • Note on the decay of acoustical waves
    • [Ral 2] _, Note on the decay of acoustical waves, Duke Math. J. 46 (1979), 799-804.
    • (1979) Duke Math. J. , vol.46 , pp. 799-804
  • 31
    • 84980143675 scopus 로고
    • Asymptotic behavior of solutions to hyperbolic partial differential equations with zero speeds
    • [Rau 1] J. Rauch, Asymptotic behavior of solutions to hyperbolic partial differential equations with zero speeds, Comm. Pure Appl. Math. 31 (1978), 431-480.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 431-480
    • Rauch, J.1
  • 32
    • 0039687341 scopus 로고
    • Local decay of scattering solutions to Schrödinger's equation
    • [Rau 2] _, Local decay of scattering solutions to Schrödinger's equation, Comm. Math. Phys. 61 (1978), 149-168.
    • (1978) Comm. Math. Phys. , vol.61 , pp. 149-168
  • 33
    • 0015992341 scopus 로고
    • Local time decay for solutions of the Schrödinger equation and the wave equation
    • [Ste] S. Steinberg, Local time decay for solutions of the Schrödinger equation and the wave equation, Archive for Rational Mech. Anal. 54 (1974), no. 2, 134-147.
    • (1974) Archive for Rational Mech. Anal. , vol.54 , Issue.2 , pp. 134-147
    • Steinberg, S.1
  • 34
    • 84980193941 scopus 로고
    • Dispersal of waves vanishing on the boundary of an exterior domain
    • [Str] W. A. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math. 28 (1975), 265-278.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 265-278
    • Strauss, W.A.1
  • 35
    • 0000377356 scopus 로고
    • A necessary condition for the well-posedness of the Cauchy problem for a certain class of evolution equations
    • [Tak] J. Takeuchi, A necessary condition for the well-posedness of the Cauchy problem for a certain class of evolution equations, Proc. Japan Acad. Ser.A Math. Sci. 50 (1974), 133-137.
    • (1974) Proc. Japan Acad. Ser.A Math. Sci. , vol.50 , pp. 133-137
    • Takeuchi, J.1
  • 36
    • 84980143603 scopus 로고
    • Grazing rays and reflection of singularities of solutions to wave equations
    • [Tay] M. Taylor, Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure and Appl. Math. 29 (1976), 1-38 and 463-481; II (systems), Comm. Pure and Appl. Math. 29 (1976), 463-481.
    • (1976) Comm. Pure and Appl. Math. , vol.29 , pp. 1-38
    • Taylor, M.1
  • 37
    • 84980140251 scopus 로고
    • II (systems)
    • [Tay] M. Taylor, Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure and Appl. Math. 29 (1976), 1-38 and 463-481; II (systems), Comm. Pure and Appl. Math. 29 (1976), 463-481.
    • (1976) Comm. Pure and Appl. Math. , vol.29 , pp. 463-481
  • 38
    • 0011495868 scopus 로고
    • Behavior of the solution of the Cauchy problem for a hyperbolic equation as t → ∞
    • [V 1] B. R. Vainberg, Behavior of the solution of the Cauchy problem for a hyperbolic equation as t → ∞, Math. USSR-Sbornik 7 (1969), no. 4, 533-567.
    • (1969) Math. USSR-Sbornik , vol.7 , Issue.4 , pp. 533-567
    • Vainberg, B.R.1
  • 39
    • 0000814357 scopus 로고
    • On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems
    • [V 2] _, On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems, Math. USSR-Sbornik 21 (1973), no. 2, 221-239.
    • (1973) Math. USSR-Sbornik , vol.21 , Issue.2 , pp. 221-239
  • 40
    • 84957156702 scopus 로고
    • On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t → ∞ of solutions of non-stationary problems
    • [V 3] _, On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t → ∞ of solutions of non-stationary problems, Russian Math. Surveys 30 (1975), no. 2, 1-58.
    • (1975) Russian Math. Surveys , vol.30 , Issue.2 , pp. 1-58
  • 41
    • 0003676725 scopus 로고
    • Moscow University Press, (Russian); English translation: Gordon and Breach Science Publishers, New York-London
    • [V 4] _, Asymptotic methods in equations of mathematical physics, Moscow University Press, 1982 (Russian); English translation: Gordon and Breach Science Publishers, New York-London, 1989.
    • (1982) Asymptotic Methods in Equations of Mathematical Physics
  • 43
    • 0011406355 scopus 로고
    • The initial-boundary value problem for the wave equation in an exterior domain with spherical boundary
    • Abstract No.564-20
    • [Wi] C. Wilcox, The initial-boundary value problem for the wave equation in an exterior domain with spherical boundary, Amer. Math. Soc. Not., Abstract No.564-20 6 (1959).
    • (1959) Amer. Math. Soc. Not. , vol.6
    • Wilcox, C.1
  • 44
    • 0011406356 scopus 로고
    • The decay of solutions of the initial-boundary value problem for hyperbolic equations
    • [Za] E. C. Zachmanoglou, The decay of solutions of the initial-boundary value problem for hyperbolic equations, J. Math. Anal. Appl. 13 (1966), 504-515.
    • (1966) J. Math. Anal. Appl. , vol.13 , pp. 504-515
    • Zachmanoglou, E.C.1
  • 45
    • 0001770301 scopus 로고
    • Reconstruction of singularities for solutions of Schrödinger equations
    • [Ze] S. Zelditch, Reconstruction of singularities for solutions of Schrödinger equations, Comm. Math. Phys. 90 (1983), 1-26.
    • (1983) Comm. Math. Phys. , vol.90 , pp. 1-26
    • Zelditch, S.1


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