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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