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Asymptotic behavior of solutions of a model derived from the 1‐D Keller–Segel model on the half line
- Source :
- Mathematical Methods in the Applied Sciences. 40:2649-2659
- Publication Year :
- 2016
- Publisher :
- Wiley, 2016.
-
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 of l > 0. In this case, the solution to the problem tends to a conserved stationary solution in an exponential decay rate, which is a very different result from the case of l
- Subjects :
- General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
Half-space
01 natural sciences
010101 applied mathematics
symbols.namesake
Green's function
symbols
Boundary value problem
Half line
0101 mathematics
Exponential decay
Stationary solution
Constant (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 10991476 and 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........3e9833cbf553e7ef37cb419ebd96d6db