# Asymptotic Convergence of Solutions for One-Dimensional Keller-Segel Equations.

@article{Iwasaki2020AsymptoticCO, title={Asymptotic Convergence of Solutions for One-Dimensional Keller-Segel Equations.}, author={Satoru Iwasaki and Koichi Osaki and Atsushi Yagi}, journal={arXiv: Analysis of PDEs}, year={2020} }

The second and third authors of this paper have constructed in [14] finite-dimensional attractors for the one-dimensional Keller-Segel equations. They have also remarked in [14, Section 7] that, when the sensitivity function is a linear function, the equations admit a global Lyapunov function. But at that moment they could not show the asymptotic convergence of solutions. This paper is then devoted to supplementing the results of [14, Section 7] by showing that, as $t \to \infty$, every…

## One Citation

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

- Mathematics
- 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…

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