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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 4

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

Yumi Yahagi
• Department of Mathematical Informatics, Tokyo University of Information Sciences, 4-1 Onaridai, Wakaba-ku, Chiba City, Japan
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Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0150

## 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.

MSC 2010: Primary 35A01, 35A02; Secondary 60H30

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Accepted: 2017-06-13

Published Online: 2018-08-06

Published in Print: 2018-08-28

Communicated by Giuseppe Di Fazio

Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 845–866, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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