Startseite Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
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Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients

  • Yumi Yahagi EMAIL logo
Veröffentlicht/Copyright: 6. August 2018
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Abstract

A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved. The main method to construct the mild solution is an argument of successive approximations by means of strongly continuous semi-groups.

  1. Communicated by Giuseppe Di Fazio

Acknowledgement

The author expresses her deep gratitude to Prof. Sergio Albeverio who gives her insightful comments and suggestions on this paper. Prof. Kiyomasa Narita is also deely acknowledged for the beneficent discussions from the point of view of probabilistic theory. She has to express her deep thanks to Prof. Noriaki Yamazaki for his accurate advice on the present research. The author would like to offer her thanks to Prof. Atsushi Yagi and Prof. Koichi Osaki who notice her the existence of the important papers [1] and [17]. She also expresses her sincere thanks to Prof. Michael Winkler for giving her his benefit papers. Prof. Minoru W. Yoshida, who discusses with the author on the fundamental structure of the present problem, is acknowledged. Finally she should acknowledge the constructive comments of the referee, which led to the substantial improvements of the paper.

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Received: 2016-11-22
Accepted: 2017-06-13
Published Online: 2018-08-06
Published in Print: 2018-08-28

© 2018 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 26.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0150/pdf
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