Universität zu Köln

Horstmann, Dirk (2013). Self-similar radial solutions to a class of strongly coupled reaction-diffusion systems with cross-diffusion. Hiroshima Math. J., 43 (3). S. 305 - 334. HIGASHI: HIROSHIMA UNIV, GRAD SCH SCI. ISSN 0018-2079

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Abstract

This paper establishes some existence and nonexistence results of self-similar radial symmetric solutions to some class of strongly coupled reaction-diffusion systems with cross-diffusion. The considered class of systems allows to reduce the problem to a single equation with exponential source terms. Using the famous Mountain Pass Theorem and some smallness conditions on the system parameters it is possible to generalize wellknown results on self-similar radial solutions for a related problem that have been established by Y. Mizutani, N. Muramoto and K. Yoshida in 1999. As an application of the results derived in the present paper it is possible to conclude the existence and nonexistence of self-similar radial solutions for multi-species chemotaxis-model in the conflict-free setting and in the presence of a conflict of interests.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Horstmann, Dirk UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-472261
DOI:	10.32917/hmj/1389102578
Journal or Publication Title:	Hiroshima Math. J.
Volume:	43
Number:	3
Page Range:	S. 305 - 334
Date:	2013
Publisher:	HIROSHIMA UNIV, GRAD SCH SCI
Place of Publication:	HIGASHI
ISSN:	0018-2079
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MODELING CHEMOTAXIS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47226