非線形解析セミナー


慶應義塾大学 理工学部 矢上キャンパス

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次回のセミナー

日時 6月20日(水) 16時45分〜
場所 14棟631A/B(創想館6階ミーティング1A/1B)
講演者 Professor Shih-Hsien Yu (National University of Singapore)
講演題目 Wave motions around a 2-D viscous Burgers' shock profile
講演要旨 In this talk we introduce the Laplace wave trains to form a basis for the 2-D wave scattering around the 2-D inviscid Burgers' shock wave for the viscous Burgers' profile for a 2-D Burgers' equation. With all those wave trains around the inviscid shock wave, one can construct the wave trains for the problem linearized around the viscous shock profile. After the complete structure of the wave scattering in terms of the Laplace wave train, one can invert the wave train information into a pointwise space-time structure of the Green's function for the problem linearized around the Burgers' shock profile. With the pointwise structure of the Green's function, the nonlinear wave scattering follows.


今後の予定

日時 6月22日(金) 16時45分〜
場所 14棟733(創想館7階ミーティング3)
講演者 Professor Yue-Jun Peng (University of Clermont Auvergne)
講演題目 Stability of non-constant equilibrium solutions for Euler-Maxwell systems
講演要旨 Euler-Maxwell systems are fluid models arising in plasma physics. In both isentropic and non-isentropic cases, such systems admit non-constant steady-state solutions with zero velocity. For the Cauchy problem or the periodic problem with initial data near the steady-states, we show global existence and the convergence of smooth solutions toward these states as the time goes to infinity. In the proof of the above result, we mainly use three techniques to yield energy estimates. These techniques are the choice of symmetrizer of the systems, the existence of anti-symmetric matrices and an induction argument on the order of space-time derivatives of solutions.

日時 6月29日(金) 16時45分〜
場所 14棟733(創想館7階ミーティング3)
講演者 水町 徹 氏(広島大・総合科学)
講演題目 On transverse stability of line solitary waves of the Benney-Luke equation
講演要旨 空間2次元のBenney-Luke方程式の線状孤立波の横断安定性について講演する。Benney-Luke方程式はKP方程式同様、3次元水面波の長波長近似モデルである。本講演では表面張力の弱い場合に、線状孤立波が線形安定になることを紹介し、線状孤立波の変調を記述するmodulation equationの導出を行う。

日時 7月11日(水) 16時〜17時00分
場所 14棟631A/B(創想館6階ミーティング1A/1B)
講演者 Professor Snorre Christiansen (University of Oslo)
講演題目 A justification of the definition of curvature in Regge Calculus
講演要旨 Regge calculus was introduced in 1961 as a coordinate free and discrete analogue of Einstein's theory of gravitation. Yet, in spite of its beautiful geometric features, the bulk of numerical computations in general relativity is, as of today, carried out by other methods, probably because of a lack of understanding of its stability and convergence properties. Surprisingly, Regge defined a curvature of simplicial manifolds, equipped with a piecewise constant metric, with a partial continuity requirement between simplices. I will provide a justification of this definition by a smoothing procedure: the curvature of the smoothened metrics converges to the curvature defined combinatorially by Regge, in the sense of measures, as the smoothing parameter goes to zero.

日時 7月11日(水) 17時15分〜18時15分
場所 14棟631A/B(創想館6階ミーティング1A/1B)
講演者 Professor Mark Groves (University of Saarlandes)
講演題目 Small-amplitude static periodic patterns at a fluid-ferrofluid interface
講演要旨 We establish the existence of static doubly periodic patterns (in particular rolls, squares and hexagons) on the free surface of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. A novel formulation of the ferrohydrostatic equations in terms of Dirichlet-Neumann operators for nonlinear elliptic boundary-value problems is presented. We demonstrate the analyticity of these operators in suitable function spaces and solve the ferrohydrostatic problem using an analytic version of Crandall-Rabinowitz local bifurcation theory. Criteria are derived for the bifurcations to be sub-, super- or transcritical with respect to a dimensionless physical parameter.

日時 7月20日(金) 16時45分〜
場所 14棟733(創想館7階ミーティング3)
講演者 井口 達雄 氏(慶應・理工)
講演題目 Initial value problem to a shallow water model with a floating solid body
講演要旨 In this talk we are concerned with the well-posedness of the initial value problem to a shallow water model for two-dimensional water waves with a floating solid body. We consider three cases: the body is fixed, the motion of the body is prescribed, and the body moves freely according to Newton's laws. The difficulty of the analysis comes from the fact that we have to treat the contact points, where the water, the air, and the solid body meet. This model yields a new type of free boundary problems for a quasilinear hyperbolic system. We will report that the initial value problem to this model is in fact well-posed. This result is based on the joint research with David Lannes at University of Bordeaux.



 セミナー世話人:
 井口 達雄(慶應義塾大学 理工学部 数理科学科)
 曽我 幸平(慶應義塾大学 理工学部 数理科学科)

 連絡先:
 井口 達雄 Tel: (045)566-1814 E-mail: iguchi@math.keio.ac.jp
 曽我 幸平 Tel: (045)566-1633 E-mail: soga@math.keio.ac.jp


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更新日: 2018年6月16日