Wave Seminar Asymptotic behavior of the solutions to some Schr\"{o}dinger equations including subcritical dissipative nonlinearities
 Date

20070713 16:00 
20070713 17:30
 Place
 Faculty of Science Building #4 Room 409

Speaker/Organizer
 Naoyasu Kita (University of Miyazaki)

 This work is the collaboration with Akihiro Shimomura(Gakusyuin University). We consider the Cauchy problem of someSchr\"{o}dinger equations including subcritical dissipativenonlinearites, where the space dimension is limited to one.Our aim in this talk is to observe largetime asymptotic behaviors ofthe solutions, which was intensively studied by many mathematicians ifthe power of nonlinearity is critical (in other words, cubic) orsupercritical. On the other hand, the subcritical case has not beenconsidered so frequently because the nonlinearity is believed to badlydecay. However, by imposing the dissipative structure on thenonlinearity, it is possible to clarify not only the decay rate of thesolution in the uniform norm but also its asymptotic form. Our argumentis largely based on HayashiNaumkin's method, but somewhat delicatetreatment of the nonlinear structure is required.
http://coe.math.sci.hokudai.ac.jp/sympo/wave/index_en.html