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November 2013 Self-similar radial solutions to a class of strongly coupled reaction-diffusion systems with cross-diffusion
Dirk Horstmann
Hiroshima Math. J. 43(3): 305-333 (November 2013). DOI: 10.32917/hmj/1389102578

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.

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Dirk Horstmann. "Self-similar radial solutions to a class of strongly coupled reaction-diffusion systems with cross-diffusion." Hiroshima Math. J. 43 (3) 305 - 333, November 2013. https://doi.org/10.32917/hmj/1389102578

Information

Published: November 2013
First available in Project Euclid: 7 January 2014

zbMATH: 1300.34027
MathSciNet: MR3161320
Digital Object Identifier: 10.32917/hmj/1389102578

Subjects:
Primary: 35J20, 35K40, 35K57
Secondary: 35Q60, 92C17

Rights: Copyright © 2013 Hiroshima University, Mathematics Program

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Vol.43 • No. 3 • November 2013
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