Dynamics in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting

讲座时间 Datetime: 2022年7月15日，星期五，9:00—10:30

地点 Venue: 腾讯线上会议：523-648-829

主持人 Host：唐德

报告人 Speaker: 沈文仙

单位 Affiliation:美国奥本大学

报告摘要 Abstract:

Chemotaxis, the directed movement of biological cells or organisms in response to certain chemicals in their environments, is a prominent feature in the organization of many biological populations. One of

the central problems on chemotaxis models is whether solutions blow up in fifinite time or exist globally. This talk is concerned with the dynamics of parabolic-elliptic chemotaxis models with singular sensitivity and logistic source for one species and the dynamics of parabolic-parabolic-elliptic chemotaxis models with singular sensitivity and Lotka-Volterra Type Competition Terms for two species. Among others, it will be shown that in any space dimensional setting, classical solutions with given positive initial data exist globally without any restriction on the parameters. Under some conditions on the parameters, it will be shown that globally defifined positive classical solutions are bounded above and below by some positive constants. It also proves the existence of positive entire solutions of such chemotaxis models in

heterogeneous media.