Singular limits of chemotaxis-growth model
The author studies a system of the form NEWLINE\[NEWLINE\left.\begin{aligned} & u_t= ab\Delta u+\nabla\cdot (u\nabla X(v))+af(u,v)=0\\ & V_t-\varepsilon c(\Delta v-g(u,v))=0\end{aligned}\right\}\quad \text{in }\mathbb{R}^N\times (0,\infty)NEWLINE\]NEWLINE with \(f(u,v)=(u^2-1)(u-\mu)+\sigma v\), \(g(u,v)=\gamma v-u\), \(a=\frac{1}{\varepsilon^2}\), \(c=\frac 1\varepsilon\), \(b=\varepsilon^2\) or \(a=c=\frac 1\varepsilon\), \(b=\varepsilon^2\). The behavior as \(\varepsilon\to 0\) is then studied.
scientific article; zbMATH DE number 1697583