Upcoming

第125回

日時 Time: 2025年3月19日（水）16:30〜18:00
場所 Place: 自然科学5号館223室
NST Hall 5, room 223
講演者 Speaker: Gilbert Peralta (University of the Philippines Baguio)
タイトル Title: Optimal Control for the Stationary Navier-Stokes Equation Involving the Pressure
概要 Abstract: We consider optimal control problems for the two-dimensional stationary Navier-Stokes equation with observations involving the pressure. For point observations, it is known that such problems give rise to PDEs with measure data for the corresponding adjoint equation. In our analysis, we will examine the state equation locally near a regular (non-singular) solution. Roughly speaking, regular solutions are those that yield topological isomorphisms for the linearized operators and consequently lead to the uniqueness of solutions within a certain neighborhood. Local optimality systems for such control problems will be presented.

第124回

日時 Time: 2025年3月12日（水）16:00〜18:15
場所 Place: 自然科学５号館数学棟４階コロキウム
NST Hall 5, Math building, 4th floor, Colloqium room
Zoom registration: https://forms.gle/y876CNxkiyUdyoUy9

講演1: 16:00–17:00

講演者 Speaker: Yoshiho AKAGAWA (Gifu KOSEN(NAtional Institute of Technology))
タイトル Title: An evolution inclusion describing strain-hardening phenomenon
概要 Abstract: Strain-hardening is a phenomenon that results from elasto-plastic deformation. This phenomenon makes additional deformation difficult as plastic deformation progresses.In 1976, Duvaut and Lions introduced a prototype model of elasto-plasticity. The essential idea of this model is to characterise elasto-plastic deformation by imposing a constraint on the deviatoric part of the stress tensor. We describe strain-hardening by allowing the constraint to depend on an unknown function. The unknown dependencies of the constraint are the crucial points of this model. As one of them, the parallel shift of the constraint plays an important role. In the case when the parallel shift depends on time nonlocally or some unknowns, then the model represents a more realistic phenomenon. This system is related to Moreau’s sweeping process and is formulated as an evolution inclusion governed by a time-dependent subdifferential.

講演2: 17:15–18:15

講演者 Speaker: Megumi SANO (Hiroshima Univ.)
タイトル Title: Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
概要 Abstract: We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the subcritical radial Sobolev spaces. Our inequality converges to the original Trudinger-Moser inequality including the optimal exponent and the concentration limit in some sense. Finally, we consider applications of our inequality to elliptic and parabolic problems with exponential nonlinearity.This is a joint work with Masahiro Ikeda(Osaka Univ.) and Koichi Taniguchi(Shizuoka Univ.).

第123回

日時 Time: 2025年1月6日（月）16:30〜18:00
場所 Place: 自然科学５号館研究棟2階 209A室 + Zoom
Natural Science and Technology Hall 5, 2nd floor, Room 209A
Zoom registration: https://kanazawa-university.zoom.us/meeting/register/tZMtdeGprTItGdSVnSVyL2oVcqme0N4TEjkW
講演者 Speaker: Philip Schrader（Murdoch University）
タイトル Title: Curve shortening by Sobolev gradient flow
概要 Abstract: The classical curve shortening flow, or one-dimensional mean curvature flow, is the gradient descent of the length functional on curves when the gradient is taken with respect to a parametrisation invariant L^2 metric. In this talk I will discuss the gradient flows of length with respect to a family of parametrisation invariant Sobolev H^1 metrics with different degrees of homogeneity. The family of flows all turn out to be equivalent under time reparametrisations. Solutions preserve embeddedness, converge to points and appear to become round while converging, like the classical flow. But unlike the classical flow, we do not encounter singularities.

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セミナーの趣旨

2013年4月，金沢大学の偏微分方程式研究者有志が集まり本セミナーを企画しました。各回の話題は，偏微分方程式の理論的な側面を中心に，セミナー幹事の関心に従い大らかに選択しています。参加者がセミナーを十分楽しみ，勉強し，新しい発見を得られるように，各回の最初の20分から30分程度，講演者の方にはその話題への導入となるような解説をお願いしています。ご関心がある方はどなたでもご自由にご参加ください。どうぞよろしくお願いいたします。

セミナー幹事 Organizers

Patrick van Meurs・大塚浩史・小俣正朗・蚊戸宣幸・木村正人・榊原航也・Thomas Geert De Jong・野津裕史・橋本伊都子・Norbert Pozar・Julius Fergy Tiongson Rabago

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