Title: Global solution to the Cauchy problem of fractional drift diffusion system with higher order nonlinearity
Speaker: Prof. Yanbin Tang ( Huazhong University of Science and Technology )
Time: Tue, Apr.13 2021, PM: 15:00-16:00
Location: Tencent Conference
Meeting Number: 662 301 459
Inviter: Prof. Yongsheng Li
Abstract:
In this talk we consider the global existence and asymptotic behavior of mild solutions to the Cauchy problem of fractional drift diffusion system with higher order nonlinearity. Using the properties of fractional heat semigroup and the classical estimates of fractional heat kernel, we first prove the global-in-time existence and uniqueness of the mild solutions in the frame of mixed time-space Besov space with multi-linear continuous mappings. Then we show the asymptotic behavior of the solution to equations with higher order nonlinearity by the method of multi-linear operator.