A 3-component system of competition and diffusion
The authors discuss the existence of non-constant steady states of a system of the form \[ \frac{\partial u_ i}{\partial t}=d_ i\frac{\partial^ 2u_ i}{\partial x^ 2}+(r_ i- \sum^{N}_{j=1}a_{ij}u_ j)u_ i,\quad x\in (0,1),\quad t\in (0,\infty),\quad i=1,...,N, \] subject to von Neumann boundary conditions, where \(d_ i\), \(r_ i\) and \(a_{ij}\) are nonnegative constants. In particular they consider the case \(N=3.\) Using singular perturbation techniques they show that under certain conditions non constant solutions may exist.
scientific article; zbMATH DE number 3997604