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math.AP2021
Optimal decay rates and space-time analyticity of solutions to the Patlak-Keller-Segel equations
Cong Wang, Yu Gao, Xiaoping Xue
Based on some elementary estimates for the space-time derivatives of the heat kernel, we use a bootstrapping approach to establish the optimal decay rates for the $L^q(\mathbb{R}^d…
math.AP2020
Global existence and spatial analyticity for a nonlocal flux with fractional diffusion
Yu Gao, Cong Wang, Xiaoping Xue
In this paper, we study a one dimensional nonlinear equation with diffusion for and . We use a viscous-splitting algorithm to…