知识与财富的链接
考虑一个模拟趋化现象的广义双曲-抛物系统的Cauchy问题,当动能函数为非线性函数且初始值具有小的L~2能量但其H~2能量可能任意大时,得到了全局光滑解的存在性和渐近行为.这些结果推广了以前的关于动能函数为线性函数或初始值具有小的H~2能量情形下的相关结果,首次获得了关于全局光滑大解方面的结果.这些结果的证明基于构造一个新的非负凸熵和做精细的能量估计.
The authors establish the existence and the asymptotic behavior of global smooth solutions to the Cauchy problem for a generalized hyperbolic-parabolic system modeling chemotaxis with the nonlinear kinetic function and smooth initial data which have small L~2-norm energy,but possibly large H~2-norm energy.These results generalize previous related results on smooth solutions for the kinetic function being linear or H~2-norm of the initial data being sufficiently small,and are first obtained for global smooth solutions with arbitrarily large H~2-norm.The proof is based on constructing a new nonnegative convex entropy and making delicate energy estimates.