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| We consider a chemotaxis system with logarithmic sensitivity and non-diffusing chemical substance.
When the chemotatic sensitivity constant is in some interval, the existence of spatially bounded global solutions to the system was proved by Ahn and Kang.
This talk gives the same result for any chemotatic sensitivity constant, assuming the smallness condition on the initial data.
Although Ahn and Kang made use of a entropy functional, we achieve the result by using two standard theorems: the small data global existence theorem, in which solutions are spatially bounded in a weak sense, and the local existence theorem, in which solutions are spatially bounded. |
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