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On singular limit of a nonlinear $p$-order equation related to Cahn-Hilliard and Allen-Cahn evolutions
Energy methods for Hartree type equations with inverse-square potentials
1. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
References:
[1] |
H. Bahouri, J.-Y. Chemin and R. Danchin, "Fourier Analysis and Nonlinear Partial Differential Equations," Grundlehren der Mathematischen Wissenschaften, 343, Springer, Heidelberg, 2011.
doi: 10.1007/978-3-642-16830-7. |
[2] |
N. Burq, F. Planchon, J. Stalker and A. S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential, J. Funct. Anal., 203 (2003), 519-549.
doi: 10.1016/S0022-1236(03)00238-6. |
[3] |
N. Burq, F. Planchon, J. Stalker and A. S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay, Indiana Univ. Math. J., 53 (2004), 1665-1680.
doi: 10.1512/iumj.2004.53.2541. |
[4] |
T. Cazenave, "Semilinear Schrödinger Equations," Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, 2003. |
[5] |
T. Cazenave and F. B. Weissler, The Cauchy problem for the nonlinear Schrödinger equation in $H^1$, Manuscripta Math., 61 (1988), 477-494.
doi: 10.1007/BF01258601. |
[6] |
J. M. Chadam and R. T. Glassey, Global existence of solutions to the Cauchy problem for time-dependent Hartree equations, J. Math. Phys., 16 (1975), 1122-1130.
doi: 10.1063/1.522642. |
[7] |
J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z., 170 (1980), 109-136.
doi: 10.1007/BF01214768. |
[8] |
E. H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems, Comm. Math. Phys., 53 (1977), 185-194.
doi: 10.1007/BF01609845. |
[9] |
N. Okazawa, T. Suzuki and T. Yokota, Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials, Appl. Anal., 91 (2012), 1605-1629.
doi: 10.1080/00036811.2011.631914. |
[10] |
N. Okazawa, T. Suzuki and T. Yokota, Energy methods for abstract nonlinear Schrödinger equations, Evolution Equations and Control Theory, 1 (2012), 337-354.
doi: 10.3934/eect.2012.1.337. |
[11] |
V. Pierfelice, Weighted Strichartz estimates for the Schrödinger and wave equations on Damek-Ricci spaces, Math. Z., 260 (2008), 377-392.
doi: 10.1007/s00209-007-0279-0. |
show all references
References:
[1] |
H. Bahouri, J.-Y. Chemin and R. Danchin, "Fourier Analysis and Nonlinear Partial Differential Equations," Grundlehren der Mathematischen Wissenschaften, 343, Springer, Heidelberg, 2011.
doi: 10.1007/978-3-642-16830-7. |
[2] |
N. Burq, F. Planchon, J. Stalker and A. S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential, J. Funct. Anal., 203 (2003), 519-549.
doi: 10.1016/S0022-1236(03)00238-6. |
[3] |
N. Burq, F. Planchon, J. Stalker and A. S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay, Indiana Univ. Math. J., 53 (2004), 1665-1680.
doi: 10.1512/iumj.2004.53.2541. |
[4] |
T. Cazenave, "Semilinear Schrödinger Equations," Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, 2003. |
[5] |
T. Cazenave and F. B. Weissler, The Cauchy problem for the nonlinear Schrödinger equation in $H^1$, Manuscripta Math., 61 (1988), 477-494.
doi: 10.1007/BF01258601. |
[6] |
J. M. Chadam and R. T. Glassey, Global existence of solutions to the Cauchy problem for time-dependent Hartree equations, J. Math. Phys., 16 (1975), 1122-1130.
doi: 10.1063/1.522642. |
[7] |
J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z., 170 (1980), 109-136.
doi: 10.1007/BF01214768. |
[8] |
E. H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems, Comm. Math. Phys., 53 (1977), 185-194.
doi: 10.1007/BF01609845. |
[9] |
N. Okazawa, T. Suzuki and T. Yokota, Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials, Appl. Anal., 91 (2012), 1605-1629.
doi: 10.1080/00036811.2011.631914. |
[10] |
N. Okazawa, T. Suzuki and T. Yokota, Energy methods for abstract nonlinear Schrödinger equations, Evolution Equations and Control Theory, 1 (2012), 337-354.
doi: 10.3934/eect.2012.1.337. |
[11] |
V. Pierfelice, Weighted Strichartz estimates for the Schrödinger and wave equations on Damek-Ricci spaces, Math. Z., 260 (2008), 377-392.
doi: 10.1007/s00209-007-0279-0. |
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