【摘要】 讨论以下一类具有Logistic源项的趋化方程组■证明齐次Neumann初边值问题的全局经典解的第一个分量关于空间变量积分具有一个正的下界,表明细胞种群作为一个整体总是持续存在的.更准确地说,对于这个方程组的任意非平凡非负全局经典解,存在一个常数m_*>0,使得对任意的t>0,有■,其中χ、r和μ都为正常数.更多还原

【Abstract】 This paper studies the dynamical properties of the chemotaxis system with Logistic source■ proving that the integral of the space variable for the first component of the global classical solutionunder homogeneous Neumann boundary conditions has a positive lower bound.The main result shows that the clonal cell population as a whole always exists. More precisely, it is shown that for any nonnegative global classical solution of this system with u?0, one can find m_*>0 such that■ for all t>0, where χ, r and μ are positive constants.更多还原