| Abstract: |
| In Keller--Segel chemotaxis models, a sensitivity function, sometimes called chemotactic potential, describes the variation of chemotactic intensity due to the change of chemical concentration. Though the choice of sensitivity functions depends on biological relevance that one tries to model, logarithmic function arises as a natural and suitable candidate in the spirit of the experimental Weber--Fechner law which states that, the perceived physical stimulus is proportional to logarithm of its actual intensity. In this talk, we present our recent results on the global stability in several Keller--Segel models with logarithmic sensitivity. To be precise, we show that the equilibrium is globally stable under one of the following conditions: i) chemotaxis rate is negative (chemo--repulsion), ii) chemotaxis rate is small (weak chemo--attraction) or iii) cellular population decays linearly (for both repulsion and attraction). Therefore, cellular aggregation is impossible in each of the three cases. This talk is based on joint works with Lin Chen and Fanze Kong. |
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