Le Chen

Chemotaxis models with signal-dependent sensitivity and a logistic-type source, III: Bifurcation and spike-like solutions

This third paper in a series on a parabolic-elliptic chemotaxis model studies bifurcation of positive constant equilibria in one space dimension. We consider $$ \left\{ \begin{array}{ll} u_t=\Delta u-\chi_0\nabla\cdot\left(\frac{u^m}{(1+v)^\beta}\nabla v\right)+au-bu^{1+\alpha},&x\in\Omega,\\ 0=\Delta v-\mu v+\nu u^\ga...