PDE Seminar (2019/4/26): Critical exponent for nonlinear damped wave equations with non-negative potential in 3D

Date
2019-4-26 16:30 - 2019-4-26 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Hideo Kubo (Hokkaido University)
 
In this talk, I'd like to present a result on the initial value problem for nonlinear damped wave equations with non-negative potential in three space dimensions which was obtained in collaboration with Professor V. Georgiev and Professor K. Wakasa. We found that there exists possible interaction among the sub-principal part of the linear wave equation which has an impact on the critical exponent of the corresponding nonlinear problem with small initial data. The main new phenomenon is that certain relation among the sub-principal part may cause very strong jump of the critical Strauss exponent in 3D to the critical Strauss exponent in 5D for the standard wave equation. In this work, we introduced a weaker weight for the solution employed in the case of the standard wave equation, which enable us to treat the damped wave equations with non-negative potential.