关于抛物-抛物Keller-Segel类模型的全局解和渐近性

The Global Solution and Asymptotic Behavior of Parabolic-Parabolic Keller-Segel Type Model

该文考虑了抛物-抛物型Keller-Segel型模型,通过Neumann热半群获得了关于ρ依赖于χ的梯度不等式,同时得到了||ρ(·,t)||L1(Ω),||(·,t)||L∞(Ω)关于时间t的收敛性.它揭示了精子的质量将收敛到初始精卵细胞的差,卵子全部受精,化学物质的浓度最终耗尽.同时化学物质的耗尽也伴随着卵细胞全部受精.它表明了化学物质的浓度在珊瑚礁受精过程中起着非常重要的作用.

This paper concerns the parabolic-parabolic Keller-Segel type model.By making use of the Neumann heat semigroup,the asymptotic inequality on the gradient of p depending on the chemotaxis signal χ is derived.Meanwhile,the convergence results on ||ρ(·,t)||L1(Ω),||(·,t)||L∞(Ω)have also been obtained.It reveals that mass of sperm will tend to the initial difference between sperm and eggs mass in the process of evolution,eggs are all fertilized and the concentration of the chemical substance will be also exhausted eventually.At the same time,the depletion of chemical substance is accompanied by complete fertilization of eggs.It illustrates that concentration of the chemical substance plays a relevant role in the fertilization process of corals.