Mathematics – Analysis of PDEs
Scientific paper
2011-10-28
Mathematics
Analysis of PDEs
Scientific paper
In this paper, we investigate large amplitude solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. For the Cauchy problem and initial-boundary value problem, the global unique solvability is proved based on the energy method. In particular, our main purpose is to investigate the convergence rates as the diffusion parameter $\epsilon$ goes to zero. It is shown that the convergence rates in $L^\infty$-norm are of the order $(\epsilon)$ and $O(\epsilon^{3/4})$ corresponding to the Cauchy problem and the initial-boundary value problem respectively.
Peng Hongyun
Ruan Lizhi
Zhu Changjiang
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