2016
DOI: 10.1002/mma.4189
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Asymptotic behavior of solutions of a model derived from the 1‐D Keller–Segel model on the half line

Abstract: In this paper, we are interested in a model derived from the 1‐D Keller‐Segel model on the half line x >  as follows: ut−lux−uxx=−β(uvx)x,x>0,t>0,λv−vxx=u,x>0,t>0,lu(0,t)+ux(0,t)=vx(0,t)=0,t>0,u(x,0)=u0(x),x>0, where l is a constant. Under the conserved boundary condition, we study the asymptotic behavior of solutions. We prove that the problem is always globally and classically solvable when the initial data is small, and moreover, we obtain the decay rates of solutions. The paper mainly deals with the case… Show more

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