Damped wave equation with a critical nonlinearity in higher space dimensions
主 题: Damped wave equation with a critical nonlinearity in higher space dimensions
报告人: Professor Nakao Hayashi (大阪大学)
时 间: 2016-09-21 15:00-16:00
地 点: 理科一号楼1303
We consider the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity. If the space dimension is less than 3, then global in time existence of small solutions was shown in our previous work. We generalize the results to any spatial dimensions via the method of decomposition of equations into high and low frequency components when the data decay rapidly at infinity in space and small. Furthermore we present the sharp time decay estimate of solutions with a logarithmic corrections.