
Seminar on Differential Equations

主講者:

史習偉博士 (University of Minnesota)

講題:

Some results on scattering for logsubcritical and logsupercritical nonlinear wave equations

時間:

20120719
(Thu.) 16:00  17:00

地點:

數學所 722 研討室 (台大院區)

Abstract:
 We consider two problems in the asymptotic behavior of semilinear second order wave equations.
First, we consider the $\dot{H}^1_x\times L^2_x$ scattering theory for the energy logsubcritical wave equation
$$\square u={\leftu\right}^{4}ug\left(\leftu\right\right)$$
in $\mathbb{R}^{1+3}$, where $g$ has logarithmic growth at $0$. We discuss the solution with general (resp. spherically symmetric) initial data in the logarithmically
weighted (resp. lower regularity) Sobolev space.
The second problem studied here involves the energy logsupercritical wave equation
$$\square u={\leftu\right}^{4}ulo{g}^{\alpha}\left(2+{\leftu\right}^{2}\right),for0<\alpha ?\frac{4}{3}$$
in $\mathbb{R}^{1+3}$. We prove the same results of global existence and $(\dot{H}^1_x\cap \dot{H}^2_x)\times H^1_x$ scattering for the equation with a slightly
higher power of the logarithm factor in the nonlinearity than that allowed by the previous work of Tao.

  Close window 
