»ã±¨±êÌâ (Title)£ºThe Effect of Signal-dependent Motility in a Keller--Segel System of Chemotaxis(ÐźÅÒÀÀµÐԻÔÚKeller-SegelÇ÷»¯ÏµÍ³ÖеÄ×÷ÓÃ)

»ã±¨ÈË (Speaker)£º½­½Ü ¸±×êÑÐÔ± (Öйú¿ÆѧԺ¾«ÃÜÕÉÁ¿¿ÆѧÓë¼¼Êõ´´ÐÂ×êÑÐÔº)

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ25ÈÕ£¨ÖÜÈÕ£©9:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飨ID£º881-381-446 »áÒéÃÜÂ룺6789£©

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In this talk, we would like to report our recent work on a Keller¡ªSegel system of chemotaxis involving signal-dependent motility. This model was originally proposed by Keller and Segel in their seminal work in 1971, and has been used to provide a new mechanism for pattern formation in some recent Bio-physics work published in Science and PRL.

From a mathematical point of view, the model features a non-increasing signal-dependent motility function, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. We develop systematic new methods to study the well-posedness problem. The key idea lies in an introduction of an elliptic auxiliary problem which enables us to apply delicate comparison arguments to derive the upper bound of concentration. Moreover, new iteration as well as monotonicity techniques are developed to study the global existence of classical solutions and their boundedness in any dimension. It is shown that the dynamic of solutions is closely related to the decay rate of the motility function at infinity. In particular, a critical mass phenomenon as well as an infinite-time blowup was verified in the two-dimensional case if the motility is a negative exponential function.

The talk is based on my recent joint works with Kentarou Fujie (Tohoku University), Philippe Lauren?ot (University of Toulouse and CNRS), Yanyan Zhang (ECNU), and Yamin Xiao (IAPCM).