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## sw NLPDE Z~i[Kyoto University NLPDE Seminar

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### ̃Z~i[̗\Upcoming seminar

2017 N 10 6 @15:30 ` 17:30
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Takahisa Inui (Tokyo University of Science)
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The sharp upper estimate of the lifespan for the semilinear wave equation with time-dependent damping
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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 $1pp_F$. 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.

### ̃Z~i[̗\Schedules of future seminars

10 6
iȑwwꕔwȁj
Takahisa Inui (Tokyo University of Science)

10 13
Tristan Roy iÉww@Ȋwȁj
Tristan Roy (Nagoya University)

10 20
Yung-fu Fang iwCpj
Yung-fu Fang (National Cheng Kung University, Taiwan)

10 27
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Okihiro Sawada (Gifu University)