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Scattering theory for the wave equation of a Hartree type in three space dimensions
1. | Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan |
References:
[1] |
F. Asakura, Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions,, Comm. Partial Differential Equations, 11 (1986), 1459.
doi: 10.1080/03605308608820470. |
[2] |
K. Hidano, Small data scattering and blow-up for a wave equation with a cubic convolution,, Funkcialaj Ekvacioj, 43 (2000), 559.
|
[3] |
F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions,, Manuscripta Math., 28 (1979), 235.
doi: 10.1007/BF01647974. |
[4] |
P. Karageorgis and K. Tsutaya, On the asymptotic behavior of nonlinear waves in the presence of a short-range potential,, Manuscripta Math., 119 (2006), 323.
doi: 10.1007/s00229-005-0620-z. |
[5] |
P. Karageorgis and K. Tsutaya, On the Asymptotic Behavior of Solutions of the Wave Equation of Hartree Type,, in preparation., (). Google Scholar |
[6] |
P. Karageorgis and K. Tsutaya, Existence and Blow Up for A Hartree-Type Wave Equation,, in preparation., (). Google Scholar |
[7] |
H. Kubo, On Point-Wise Decay Estimates for the Wave Equation and Their Applications,, Dispersive nonlinear problems in mathematical physics, (2004), 123.
|
[8] |
G. Perla Menzala and W. A. Strauss, On a wave equation with a cubic convolution,, J. Diff. Eq., 43 (1982), 93.
doi: 10.1016/0022-0396(82)90076-6. |
[9] |
K. Mochizuki and T. Motai, On Small Data Scattering for Some Nonlinear Wave Equations,, Patterns and waves, (1986), 543.
doi: 10.1016/S0168-2024(08)70145-0. |
[10] |
K. Mochizuki, On small data scattering with cubic convolution nonlinearity,, J. Math. Soc. Japan, 41 (1989), 143.
doi: 10.2969/jmsj/04110143. |
[11] |
H. Pecher, Scattering for semilinear wave equations with small data in three space dimensions,, Math. Z., 198 (1988), 277.
doi: 10.1007/BF01163296. |
[12] |
W. A. Strauss, Nonlinear invariant wave equations,, Lecture Notes in Phys., 73 (1978), 197.
|
[13] |
W. A. Strauss and K. Tsutaya, Existence and blow up of small amplitude nonlinear waves with a negative potential,, Discrete Continuous Dynam. Systems, 3 (1997), 175.
doi: 10.3934/dcds.1997.3.175. |
[14] |
K. Tsutaya, Global existence and blow up for a wave equation with a potential and a cubic convolution,, Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th Birthday. Vol. 1, (2003), 913.
|
[15] |
K. Tsutaya, Scattering theory for a wave equation of Hartree type,, Differential & Difference Equations And Applications, (2006), 1061.
|
[16] |
K. Tsutaya, Weighted estimates for a convolution appearing in the wave equation of Hartree type,, to appear in J. Math. Anal. Appl.., (). Google Scholar |
show all references
References:
[1] |
F. Asakura, Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions,, Comm. Partial Differential Equations, 11 (1986), 1459.
doi: 10.1080/03605308608820470. |
[2] |
K. Hidano, Small data scattering and blow-up for a wave equation with a cubic convolution,, Funkcialaj Ekvacioj, 43 (2000), 559.
|
[3] |
F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions,, Manuscripta Math., 28 (1979), 235.
doi: 10.1007/BF01647974. |
[4] |
P. Karageorgis and K. Tsutaya, On the asymptotic behavior of nonlinear waves in the presence of a short-range potential,, Manuscripta Math., 119 (2006), 323.
doi: 10.1007/s00229-005-0620-z. |
[5] |
P. Karageorgis and K. Tsutaya, On the Asymptotic Behavior of Solutions of the Wave Equation of Hartree Type,, in preparation., (). Google Scholar |
[6] |
P. Karageorgis and K. Tsutaya, Existence and Blow Up for A Hartree-Type Wave Equation,, in preparation., (). Google Scholar |
[7] |
H. Kubo, On Point-Wise Decay Estimates for the Wave Equation and Their Applications,, Dispersive nonlinear problems in mathematical physics, (2004), 123.
|
[8] |
G. Perla Menzala and W. A. Strauss, On a wave equation with a cubic convolution,, J. Diff. Eq., 43 (1982), 93.
doi: 10.1016/0022-0396(82)90076-6. |
[9] |
K. Mochizuki and T. Motai, On Small Data Scattering for Some Nonlinear Wave Equations,, Patterns and waves, (1986), 543.
doi: 10.1016/S0168-2024(08)70145-0. |
[10] |
K. Mochizuki, On small data scattering with cubic convolution nonlinearity,, J. Math. Soc. Japan, 41 (1989), 143.
doi: 10.2969/jmsj/04110143. |
[11] |
H. Pecher, Scattering for semilinear wave equations with small data in three space dimensions,, Math. Z., 198 (1988), 277.
doi: 10.1007/BF01163296. |
[12] |
W. A. Strauss, Nonlinear invariant wave equations,, Lecture Notes in Phys., 73 (1978), 197.
|
[13] |
W. A. Strauss and K. Tsutaya, Existence and blow up of small amplitude nonlinear waves with a negative potential,, Discrete Continuous Dynam. Systems, 3 (1997), 175.
doi: 10.3934/dcds.1997.3.175. |
[14] |
K. Tsutaya, Global existence and blow up for a wave equation with a potential and a cubic convolution,, Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th Birthday. Vol. 1, (2003), 913.
|
[15] |
K. Tsutaya, Scattering theory for a wave equation of Hartree type,, Differential & Difference Equations And Applications, (2006), 1061.
|
[16] |
K. Tsutaya, Weighted estimates for a convolution appearing in the wave equation of Hartree type,, to appear in J. Math. Anal. Appl.., (). Google Scholar |
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