| Abstract: |
| This talk is concerned with the global existence and spatial spreading speeds in
three primary chemotaxis systems with logistic source on the whole space $\mathbb{R}^N$.
First, I will present a unified proof demonstrating global existence of positive classical solutions
of these systems can be deduced from their uniform boundedness in $L_{\rm loc}^p(\mathbb{R}^N)$
for some $p>\max\{1,\frac{n}{2}\}$. I will then provide sufficient conditions in terms of the parameters
in the systems for the global existence and boundedness of classical solutions.
Next, I will discuss the spatial spreading speeds of positive solutions with compactly supported or front-like initial functions. Special attention will be given to influence of the chemotaxis sensitivity on the propagation speeds
of such solutions. It will be shown that chemotaxis does not slow down the spatial spreading no matter
it is positive taxis or negative taxis. Some discussion will also be given on whether chemotaxis speeds up
the spatial spreading. |
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