Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 259, Issue 5, Pages 1990-2029Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.03.017
Keywords
Degn-Harrison; Fundamental properties; Stability; Nonexistence; Local and global structure
Categories
Funding
- Natural Science Foundation of China [11271236, 11401356]
- Program for New Century Excellent Talents in University of Ministry of Education of China [NCET-12-0894]
- Fundamental Research Funds for the central Universities [GK201401004]
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In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem. (C) 2015 Elsevier Inc. All rights reserved.
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