偏微分方程式セミナー(2014/5/12):The lifespan of solutions to nonlinear wave equations with weighted functions in 1D, 若狭恭平氏 (北海道大学)

開催日時
2014年   5月 12日 16時 30分 ~ 2014年   5月 12日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
若狭恭平 (北海道大学大学院理学院)
 
In 1980, T.Kato showed that a solution of the semilinear wave equations
in one space dimension blows up in finite time for any power nonliearity.
When the equation has a weighted nonlinear term, the solution exists
globally in time provided that the initial data is odd function.
On the other hand, the solution blows up in finite time provided that the
initial data is not odd function. These results were first shown by
A.Suzuki (2010). Later, Kubo & Osaka & Yazici (2013) have obtained the
sharp conditions to get the global existence and blow-up. However the
estimate for the lifespan, the maximal existence time, of solutions was
not clarified in both papers.
Our aim in this talk is to give the sharp upper and lower bounds of the
lifespan.


関連項目

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