Abstract
We study the large time behaviors of solutions to the Keller–Segel system with logarithmic singular sensitivity in the half space, where biological mixed boundary conditions are prescribed. The existence and asymptotic stability of spiky steady states of this system were proved by Carrillo et al. (2021). In this paper we obtain convergence rate of solutions towards the steady state under appropriate initial perturbations. The proofs are based on a Cole–Hopf type transformation and a weighted energy method, where the weights are artfully constructed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.