Logistic damping effect in chemotaxis models with density-suppressed motility

Abstract

This paper is concerned with a parabolic-elliptic chemotaxis model with densitysuppressed motility and general logistic source in an n-dimensional smooth bounded domain with Neumann boundary conditions. Under the minimal conditions for the density-suppressed motility function, we explore how strong the logistic damping can warrant the global boundedness of solutions, and further establish the asymptotic behavior of solutions on top of the conditions.

Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing

“…Building upon (2.12), we derive additional estimates on (v η ) η with the help of a comparison argument introduced in [6] (and subsequently developed further in [7][8][9][10]14,18,19]) and parabolic maximal regularity. Lemma 2.4.…”

Global dynamics for a chemotaxis consumption system with signal-dependent motility and logistic source

“…Global weak solutions were studied in [7]. For superlinear degradation we refer to [36,37]. Moreover, global existence of classical solutions has also been extensively investigated involving three-component signal-dependent motility models (cf.…”