Speaker :
 Dr. HsiWei Shih(University of Minnesota) 

Title :

Some results on scattering for logsubcritical and logsupercritical nonlinear wave equations 
Time :
 20120719 (Thu) 16:00  17:00 
Place : 
Seminar Room 722, Institute of Mathematics (NTU Campus) 

Abstract: 
We consider two problems in the asymptotic behavior of semilinear second order wave equations.
First, we consider the scattering theory for the energy logsubcritical wave equation
$$\square u={\leftu\right}^{4}ug\left(\leftu\right\right)$$
in , where has logarithmic growth at . 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
$$\square u={\leftu\right}^{4}ulo{g}^{\alpha}\left(2+{\leftu\right}^{2}\right),for0<\alpha \le \frac{4}{3}$$
in . We prove the same results of global existence and 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. 
