Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Daoyin He, Southeast University
Inviter:
Title:	Long Time Evolution of Semilinear Tricomi Equations
Language:	Chinese
Time & Venue:	2023.12.22 09:00-10:00 MCM110
Abstract:	We consider the global Cauchy problem for the semilinear generalized Tricomi equation \partial_t^2u-t^m?u=up with suitable initial data \left(u\left(0,\bullet\right), \partial_tu\left(0,\bullet\right)\right)=\left(u_0,u_1\right), where t\geq0, x\in\mathbb{R}^n\left(n\geq1\right), m\in\mathbb{N}, p>1. We determine a critical exponent p_{crit}\left(m,n\right)>1 such that the solution u, in general, blows up in finite time when 1<p\le p_{crit}\left(m,n\right), while the global existence result with small data is established for p>p_{crit}\left(m,n\right). This is a joint work with Prof. Yin and Prof. Witt.