Asymptotic properties of solutions to dispersive equation of Schrödinger type
HAYASHI, Nakao ; NAUMKIN, Pavel I.
J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 631-652 / Harvested from Project Euclid
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We find the asymptotic behavior for large time of solutions to the dispersive equations of Schrödinger type $u_{t}-\frac{i}{\rho} |\partial_{x}|^{\rho}u = 0, \quad (t,x) \in \bm{R} \times \bm{R},$ where   $\rho \geq 2$ . We obtain some estimates of solutions of linear problem and apply them to nonlinear problems with power nonlinearities of order $p\geq 3$ . The nonexistence of wave operator and existence of the modified wave operator for the critical nonlinearity $i\lambda |u|^{2}u$ are studied.
Publié le : 2008-07-15
Classification:  asymptotics of solutions,  dispersive equations,  nonlinear problems,  35Q55 
@article{1217884486,
     author = {HAYASHI, Nakao and NAUMKIN, Pavel I.},
     title = {Asymptotic properties of solutions to dispersive equation of Schr\"odinger type},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 631-652},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1217884486}
}

HAYASHI, Nakao; NAUMKIN, Pavel I. Asymptotic properties of solutions to dispersive equation of Schrödinger type. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  631-652. http://gdmltest.u-ga.fr/item/1217884486/