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2月演講

PDE Seminar, 成功大學數學系 吳恭儉教授
Wednesday, February 13, 11:10—15:00 數學系3樓會議室
Title: Milne Problem
Abstract: Stationary half-space solutions of the linearized Boltzmann equation with hard potential are studied by energy estimate methods. I will present existence, uniqueness and asymptotic behavior of this problem.

Colloquium, 京都大學數學系 Prof. Yoshio Tsutsumi
Thursday, February 21, 15:10—16:00 數學系3174
Title: Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term
Abstract: We consider the ill-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It has been universally used among physicists as a mathematical model for the photonic crystal fiber oscillator (see, e.g., [1]). I show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map at the origin under slightly different conditions, respectively. Physicists sometimes propose models which have strong instability from a mathematical point of view. Equation (1) is such a kind of example and it is not very clear what role the mathematical ill-posedness plays in physics. I also talk about the local unique existence of solutions in the analytic function space. This talk is based on the joint work [2] with Nobu Kishimoto, RIMS, Kyoto University. References [1] G. Agrawal, Nonlinear Fiber Optics, 4th edition, Elsevier / Academic Press, Burlington, 2007. [2] N. Kishimoto and Y. Tsutsumi, Ill-posedness of the third order NLS equation with Raman scattering term, preprint, arXiv: 1706.09111v1 [math.AP]

Colloquium, 京都大學數學系 Prof. Yoshio Tsutsumi
Thursday, February 21, 16:10—17:00 數學系3174
Title: Quasi-Invariant Gaussian Measures for NLS with Third Order Dispersion
Abstract: Invariant measures for nonlinear evolution equations have been attracted the attention of many researchers. Especially, the Gibbs measure for the Hamiltonian system is natural and important from both mathematical and physical points of view. However, the support of the Gibbs measure is determined by the Hamiltonian of the system in question and it is often a weak function space. Therefore, the Gibbs measure does not capture smooth solutions such as finite energy solutions. Recently, Tzvetkov showed the quasi-invariant property of Gaussian measures with support including smooth solutions for some nonlinear dispersive equations instead of the invariant property. It is very interesting, because the quasi-invariance might be able to replace the role of invariance. In this talk, I will talk about the quasi-invariance of certain Gaussian measures for NLS with third order dispersion. This is a joint work with Nikolay Tzvetkov (University of Cergy-Pontoise) and Tadahiro Oh (University of Edinburgh).

   
 


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國立成功大學數學系
70101 台南市大學路一號
電話︰(06) 2757575 轉 65100   傳真︰(06) 2743191
em65100[at]email.ncku.edu.tw