京都大学 NLPDE セミナー

京都大学 NLPDE セミナー
Kyoto University NLPDE Seminar

このセミナーは非線形微分方程式を中心に解析の研究に関して討論するセミナーです.

日時
毎週金曜日 Every Friday 15:30 〜 17:30
会場
京都大学 理学研究科 3 号館 251 号室 (会場へのアクセス
Room 251 at Science Building No.3, Kyoto University (map
幹事
堤誉志雄, 前川泰則, 岸本展


次回のセミナーの予定
Upcoming seminar

● 2017 年 10 月 6 日 15:30 〜 17:30
講演者
戍亥 隆恭 氏 (東京理科大学理学部第一部数学科)
Takahisa Inui (Tokyo University of Science)
講演題目
The sharp upper estimate of the lifespan for the semilinear wave equation with time-dependent damping
講演要旨
We are interested in the estimate of the lifespan for the semilinear damped wave equation with the time-dependent coefficient $(1+t)^{-\beta}$ in front of $u_t$. It is known that the critical exponent for the $L^1$ initial data is the Fujita exponent $p_F$ when $\beta \in [-1,1)$. Moreover, the estimates of the lifespan is known when $1<p<p_F$. In the critical case $p=p_F$, the upper estimate of the lifespan was obtained by Ikeda and Ogawa (2016). However, their estimate is not sharp. Recently, when $\beta=0$ and $p=p_F$, Lai and Zhou obtained the sharp upper estimate of the lifespan in [arXiv:1702.07073]. In this talk, we give the sharp upper estimate of the lifespan when $\beta \in [-1,1)$ and $p=p_F$. We remark that, when $\beta=-1$, Fujiwara, Ikeda, and Wakasugi [arXiv:1609.01035] obtained a double-exponential type lower estimate of the lifespan but it was not known whether small data blow-up holds or not. We give the sharp (i.e. the double-exponential type) upper estimate of the lifespan when $\beta=-1$. This talk is based on a joint work with Dr. Masahiro Ikeda in RIKEN.


今後のセミナーの予定
Schedules of future seminars

10 月 6 日
戍亥 隆恭 氏 (東京理科大学理学部第一部数学科)
Takahisa Inui (Tokyo University of Science)

10 月 13 日
Tristan Roy 氏 (名古屋大学大学院多元数理科学研究科)
Tristan Roy (Nagoya University)

10 月 20 日
Yung-fu Fang 氏 (国立成功大学,台湾)
Yung-fu Fang (National Cheng Kung University, Taiwan)

10 月 27 日
澤田 宙広 氏 (岐阜大学工学部)
Okihiro Sawada (Gifu University)