Existence of monotone positive solutions of a neighbour based chemotaxis model and aggregation phenomenon (Q2658633)

This article treats the one-dimensional steady state problem corresponding to the ``neighbour based'' chemotaxis model \[ \begin{cases} u_t = \nabla\cdot (\Gamma(v)\nabla u - \Gamma'(v)u\nabla v)\\ v_t = \Delta v - v +u \end{cases} \] with the cell transition probability \(\Gamma\) generalizing the choice \(\Gamma(v)=e^v\). Bifurcation theory -- the bifurcation parameter being the average of \(v\) -- is employed to find ``spiky'' steady states.