SEMINARS
Blow up of solutions to some quasilinear equations arising from water waves

2017-12-15　14:00 — 15:00

Large Conference Room

Yue Liu

Department of Mathematics, University of Texas, Arlington

xiongfeng Yang

In this talk,  the blow-up mechanism for a class of quasilinear integrable equations which could possess peakons is investigated. The dynamics of the blow-up quantity  involves interplay  between the solution $u$ and its gradient $u_x$. We provide two different approaches. The first one is based on a refined analysis on  either the evolution of $Cu \pm u_x$ or the growth rate of the relative ratio $u_x/u$. The second one isolates the truly" blowing up component from the blow-up quantity and utilizes the conservation laws to show that such a component blows up before the other component degenerates.
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