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Mathematica Slovaca

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Volume 68, Issue 4

Issues

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

Keywords: Keller-Segel system; uniformly elliptic operator

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About the article

Received: 2016-11-22

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, DOI: https://doi.org/10.1515/ms-2017-0150.

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