# Convergence to diffusion waves for solutions of 1D Keller-Segel model

@inproceedings{Liu2021ConvergenceTD, title={Convergence to diffusion waves for solutions of 1D Keller-Segel model}, author={F. L. Liu and N. G. Zhang and C. J. Zhu}, year={2021} }

In this paper, we are concerned with the asymptotic behavior of
solutions to the Cauchy problem (or initial-boundary value problem) of
one-dimensional Keller-Segel model. For the Cauchy problem, we prove
that the solutions time-asymptotically converge to the nonlinear
diffusion wave whose profile is self-similar solution to the
corresponding parabolic equation, which is derived by Darcy’s law, as in
[11, 28]. For the initial-boundary value problem, we consider two
cases: Dirichlet boundary…

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