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• W2903105512 abstract "This paper focuses on the following Keller-Segel system with singular sensitivity and logistic source $$ left{begin{array}{ll} u_t=Delta u-chinablacdot(frac{u}{v}nabla v)+ au-mu u^2,quad xin Omega, t>0, disp{ v_t=Delta v- v+u},quad xin Omega, t>0 end{array}right.eqno(star) $$ in a smoothly bounded domain $Omegasubsetmathbb{R}^N(Ngeq1)$, with zero-flux boundary conditions, where $a>0,mu>0$ and $chi>0$ are given constants. If $chi$ is small enough, then, for all reasonable regular initial data, a corresponding initial-boundary value problem for $(star)$ possesses a global classical solution $(u, v)$ which is {bf bounded} in $Omegatimes(0,+infty)$. Moreover, if $mu$ is large enough, the solution $(u, v)$ exponentially converges to the constant stationary solution $(frac{a}{mu }, frac{a}{mu })$ in the norm of $L^infty(Omega)$ as $trightarrowinfty$. To the best of our knowledge, this new result is {bf the first} analytical work for the boundedness and {bf asymptotic behavior} of Keller--Segel system with {bf singular sensitivity} and {bf logistic source} in higher dimension case ($Ngeq3$)." @default.
• W2903105512 created "2018-12-11" @default.
• W2903105512 creator A5077280174 @default.
• W2903105512 date "2018-12-06" @default.
• W2903105512 modified "2023-09-27" @default.
• W2903105512 title "Boundedness and large time behavior in a higher-dimensional Keller--Segel system with singular sensitivity and logistic source." @default.
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