第１６０回 広島数理解析セミナー （２０１２年度）
Hiroshima Mathematical Analysis Seminar No.160
日時 ： ６月２２日（金）１５：００〜１７：３０ 場所 ： 広島大学理学部 Ｂ７０７
今回は２件の講演です．
１５：００〜１６：００
講師 ：
Ruy Coimbra Char˜ao氏 （Federal University of Santa Catarina）
題目 ：
Spectral properties of a coupled system of Schr¨odinger equations with time-periodic coefficients要旨 ：
We consider a coupled system of Schr¨odinger equations with time-periodic coefficients,i ut =−∆u+V(x, t)u+g(x, t)v i vt =−∆v+W(x, t)v+g(x, t)u
on the Hilbert space H = L2(Rn)×L2(Rn), where g, V and W are periodic time-dependent potentials, with period T. We denote by (U(t, s))(t,s)∈R×R its associated propagator. The study of the spectrum of the so called Floquet operator U ≡ U(T,0) is relevant for the asymptotic behavior of the solutions U(t,0)ϕ. By using a multiplier method we establish the absence of regular eigenvectors of the Floquet operator U(T,0).
参考文献
[1] M. A. Astaburuaga, O. Bourget, V. H. Cort´es, C. Fern´andez, Floquet op- erators without singular continuous spectrum, J. Funct. Anal. 238 (2006), 489–517.
[2] R. Lavine, Commutators and scattering theory I, Repulsive interactions, Comm. Math. Phys.20(1971), 301–323. Commutators and scattering the- ory II, A class of one-body problems, Indiana Univ. Math. J. 21 (1972), 643-656.
[3] K. Yokoyama, Mourre theory for time-periodic systems, Nagoya Math. J.
149 (1998), 193–210.
１６：３０〜１７：３０
講師 ：
Cleverson Roberto da Luz氏 （Federal University of Santa Catarina）
題目 ：
Uniform decay rates of anisotropic electromagnetic/elasticity models要旨 ：
A coupled semilinear system of dynamic hyperbolic equations in electro- magnetic/elasticity in three-dimensional domains is considered. Anisotropic Maxwell equations are very special: The energy in general does not propagate along the normals to the fronts but along rays which are distinct from the normals. Thus, in these kinds of mediums the so-called permittivity and per- meability are no more scalar-valued functions but 3×3 symmetric matrices.In this talk we show decay rates of the total energy of the coupled anisotropic system provided mild dissipative effects are present. In exterior domains our main result says that in the presence of nonlinear damping, a unique solution of small initial data exists globally in time and the total energy as well as higher order energies decay at an uniform rate. In case of bounded domains the energy associated with the model decays exponentially.
広島数理解析セミナー幹事
池畠 良（広大教育） [email protected] 市原 直幸（広大工・総科）[email protected]
大西 勇（広大理） isamu [email protected] 川下 美潮（広大理） [email protected] 倉 猛（広大理） [email protected] 佐々木良勝（広大理） [email protected]
F滝本 和広（広大理） [email protected] 松本 敏隆（広大理） [email protected]
F印は本セミナーの責任者です
