Critical mass on the Keller-Segel system with signal-dependent motility

Abstract

This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility function decays exponentially, then a critical mass phenomenon similar to the minimal Keller-Segel model will arise. That is there is a number $m_{\ast }>0$, such that the solution will globally exist with uniform-in-time bound if the initial cell mass (i.e. $L^1$-norm of the initial value of cell density) is less than $m_{\ast }$, while the solution may blow up if the initial cell mass is greater than $m_{\ast }$.

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Cited by in corpus (9)

• Global boundedness of solutions to a parabolic-parabolic chemotaxis system with local sensing in higher dimensions
• On the parabolic-elliptic Keller-Segel system with signal-dependent motilities: a paradigm for global boundedness and steady states
• Boundedness in a taxis-consumption system involving signal-dependent motilities and concurrent enhancement of density-determined diffusion and cross-diffusion
• Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility
• Uniform $L^p$ estimates for solutions to the inhomogeneous 2D Navier-Stokes equations and application to a chemotaxis-fluid system with local sensing
• Global boundedness of the fully parabolic Keller-Segel system with signal-dependent motilities
• Boundedness and asymptotics of a reaction-diffusion system with density-dependent motility
• Travelling wave solutions of the density-suppressed motility model
• The Keller-Segel system with logistic growth and signal-dependent motility