| Abstract: |
| This talk is concerned with the existence, uniqueness, and stability of traveling wave solutions
to a repulsion parabolic-elliptic chemotaxis system with logistic type source.
When the chemotaxis sensitivity coefficient $\chi=0$, this system reduces to the so called Fisher-KPP equation,
which generates a monotone dynamical system, possesses a minimal wave speed $c^*$, and admits a unique monotone stable traveling wave solution connecting the positive constant solution and the zero solution
for any speed $c\ge c^*$. When $\chi\not = 0$, the system does not generate a monotone dynamical system, or comparison principle does not hold for the system, and several difficulties appear when studying traveling wave solutions to the system. In this talk, we will show that when $\chic^*$ such that the system admits a unique stable monotone traveling wave solution connecting the positive constant solution and the zero solution for any speed $c>^*_{\chi}$. Though the comparison principle does not hold for the system, it is utilized in some nontrivial way in the proof of the results stated in the above. |
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