On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis
Volume 193 / 2009
Studia Mathematica 193 (2009), 241-261
MSC: 35K57, 35B40.
DOI: 10.4064/sm193-3-2
Abstract
We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller–Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
