Self-similar solutions to a parabolic system modeling chemotaxis
This paper concerns the forward self-similar solutions to a parabolic system modeling chemotaxis \[ u_t= \nabla\cdot(\nabla u- u\nabla v),\quad \tau v_t=\Delta v+u \] in \(\mathbb{R}^2\), where \(\tau> 0\) is a constant. By a Liouville-type result and using the method of moving planes it is proved that self-similar solutions \((u,v)\) must be radially symmetric about the origin. The structure of the set of self-similar solution has been investigated.
scientific article; zbMATH DE number 1815486
scientific article