Radial spiky steady states of a flux-limited Keller-Segel model: Existence, asymptotics, and stability

This paper is concerned with the radial stationary problem of a flux-limited Keller-Segel model derived in a multidimensional bounded domain with Neumann boundary conditions. With the global bifurcation theory and Helly compactness theorem by treating the chemotactic coefficient as a bifurcation parameter, we establish the existence of nonconstant monotone radial stationary solutions and further show that the radial stationary solution will tend to a Dirac delta mass as the chemotactic coefficient tends to infinity. By using the stability criterion of Crandall and Rabinnowitz, we prove the linearized stability of bifurcating stationary solutions near the bifurcation points.

Automated summary

By treating the chemotactic coefficient as a bifurcation parameter, this paper establishes the existence of nonconstant monotone radial stationary solutions using global bifurcation theory and the Helly compactness theorem. It further shows that the radial stationary solution tends to a Dirac delta mass as the chemotactic coefficient tends to infinity. The linearized stability of bifurcating stationary solutions near the bifurcation points is also proven using the stability criterion of Crandall and Rabinnowitz.