On the parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis

Piotr Biler (1) , Lorenzo Brandolese (2)

1 Instytut Matematyczny
2 ICJ - Institut Camille Jordan

We establish new convergence results, in strong topologies, for 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.

Mots clés: chemotaxis system; local and global in time solutions; convergence of solutions; Patlak-Keller-Segel; asymptotic analysis; parabolic-parabolic

Domaines: Equations aux dérivées partielles [math.AP]; Interactions cellulaires [q-bio.CB]

Piotr Biler, Lorenzo Brandolese. On the parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis. Studia Mathematica, 2009, 193 (3), pp.241--261. ⟨hal-00270699v2⟩