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- W2945139075 abstract "We are concerned with the following full Attraction-Repulsion Keller-Segel (ARKS) system begin{equation}label{ARKS}tag{$ast$} begin{cases} u_t=Delta u-nablacdot(chi unabla v)+nablacdot(xi unabla w), &xin Omega, ~~t>0, v_t=D_1Delta v+alpha u-beta v,& xin Omega, ~~t>0, w_t=D_2Delta w+gamma u-delta w, &xin Omega, ~~t>0, u(x,0)=u_0(x),~v(x,0)= v_0(x), w(x,0)= w_0(x) & xin Omega, end{cases} end{equation} in a bounded domain $Omegasubset R^2$ with smooth boundary subject to homogeneous Neumann boundary conditions. %The parameters $D_1,D_2,chi,xi,alpha,beta,gamma$ and $delta$ are positive. By constructing an appropriate Lyapunov functions, we establish the boundedness and asymptotical behavior of solutions to the system eqref{ARKS} with large initial data. Precisely, we show that if the parameters satisfy $frac{xigamma}{chialpha}geq maxBig{frac{D_1}{D_2},frac{D_2}{D_1},frac{beta}{delta},frac{delta}{beta}Big}$ for all positive parameters $D_1,D_2,chi,xi,alpha,beta,gamma$ and $delta$, the system eqref{ARKS} has a unique global classical solution $(u,v,w)$, which converges to the constant steady state $(bar{u}_0,frac{alpha}{beta}bar{u}_0,frac{gamma}{delta}bar{u}_0)$ as $tto+infty$, where $bar{u}_0=frac{1}{|Omega|}int_Omega u_0dx$. Furthermore, the decay rate is exponential if $frac{xigamma}{chialpha}> maxBig{frac{beta}{delta},frac{delta}{beta}Big}$. This paper provides the first results on the full ARKS system with unequal chemical diffusion rates (i.e. $D_1ne D_2$) in multi-dimensions." @default.
- W2945139075 created "2019-05-29" @default.
- W2945139075 creator A5021174704 @default.
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- W2945139075 date "2019-05-15" @default.
- W2945139075 modified "2023-09-24" @default.
- W2945139075 title "Global stabilization of the full attraction-repulsion Keller-Segel system" @default.
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- W2945139075 doi "https://doi.org/10.48550/arxiv.1905.05990" @default.
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