Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source

Abstract

We consider the fully parabolic, spatially heterogeneous chemotaxis-growth system \begin{align*} \begin{cases} u_t = Δu - \nabla\cdot(u\nabla v) + κ(x)u-μ(x)u^2, \\ v_t = Δv - v + u \end{cases} \end{align*} in bounded domains $\Omega \subset {\mathbb{R}}^2$ and show that the blow-up set is contained in the set of zeroes of $\mu$.

arXiv comment16 pages

References in corpus (4)

• Finite-time blow-up in a two-dimensional Keller--Segel system with an environmental dependent logistic source
• When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?
• Corners and collapse: Some simple observations concerning critical masses and boundary blow-up in the fully parabolic Keller-Segel system
• Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source