過去の記録 ~02/07次回の予定今後の予定 02/08~

担当者 河野俊丈


16:30-18:00   数理科学研究科棟(駒場) 128号室
Hatem Zaag 氏 (CNRS/University of Paris Nord)
Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)
[ 講演概要 ]
In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.

In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.

Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.