RT Journal Article
T1 A blow-up mechanism for a chemotaxis model
A1 Herrero, Miguel A.
A1 Velázquez, J.J. L.
AB We consider the following nonlinear system of parabolic equations: (1) ut =Δu−χ∇(u∇v), Γvt =Δv+u−av for x∈B R, t>0. Here Γ,χ  and a are positive constants and BR is a ball of radius R>0 in R2. At the boundary of BR, we impose homogeneous Neumann conditions, namely: (2) ∂u/∂n=∂v/∂n=0 for |x|=R, t>0. Problem (1),(2) is a classical model to describe chemotaxis, i.e., the motion of organisms induced by high concentrations of a chemical that they secrete. In this paper we prove that there exist radial solutions of (1),(2) that develop a Dirac-delta type singularity in finite time, a feature known in the literature as chemotactic collapse. The asymptotics of such solutions near the formation of the singularity is described in detail, and particular attention is paid to the structure of the inner layer around the unfolding singularity.
PB Scuola Normale Superiore
SN 0391-173X
YR 1997
FD 1997
LK https://hdl.handle.net/20.500.14352/58709
UL https://hdl.handle.net/20.500.14352/58709
LA eng
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NO DGICYT
DS Docta Complutense
RD 7 may 2024