Long Time Evolution of Semilinear Tricomi Equations
Prof. Daoyin He
2023-12-22 9:00-10:00
MCM110
Speaker: Prof. Daoyin He (Southeast University)Time: 9:00-10:00 December 22, 2023 (Friday)
Place: MCM110
Title: Long Time Evolution of Semilinear Tricomi Equations
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.
