Biler, P. and Wu, G. (2009) Two-Dimension Chemotaxis Models with Fractional Diffusion. Mathematical Methods in the Applied Sciences, 32, 112-126.
https://doi.org/10.1002/mma.1036

has been cited by the following article:

• TITLE: Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces

  AUTHORS: Weiliang Xiao, Yu Zhang

  KEYWORDS: Well-Posedness, Gevrey Regularity, Time Decay, Besov Spaces

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.1, January 19, 2022

  ABSTRACT: In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p q ≤ ∞, and analyticity of solutions with 1 p q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.