** For more information on Asia-Pacific Analysis and PDE Seminar (JOINT), 

please visit http://www.maths.usyd.edu.au/u/Asia-Pacific-APDESeminar/ **

ABSTRACT

In this talk, I will report recent progress on global behaviors for solutions of energy subcritical defocusing semilinear wave equations with pure power nonlinearity. We prove that in space dimension 1 and 2, the solution decays in time with an inverse polynomial rate, hence giving an affirmative answer to a conjecture raised by Lindblad and Tao. In higher dimension, we obtain improved scattering results for the solutions. The proof is based on vector field method with new multipliers. These works are jointed with Dongyi Wei.