Asymptotically self-similar solutions for the parabolic system modelling chemotaxis
Volume 74 / 2006
Banach Center Publications 74 (2006), 149-160
MSC: Primary 35B40; Secondary 35K55.
DOI: 10.4064/bc74-0-9
Abstract
We consider a nonlinear parabolic system modelling chemotaxis $$ u_t = \nabla\cdot(\nabla u - u\nabla v), \quad v_t = \Delta v + u $$ in ${\mathbb R}^2$, $t > 0$. We first prove the existence of time-global solutions, including self-similar solutions, for small initial data, and then show the asymptotically self-similar behavior for a class of general solutions.
