Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 48, Issue -, Pages 326-336Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2019.01.010
Keywords
Blow up of solutions; Singular Gierer-Meinhardt systems; Dirichlet boundary conditions
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Funding
- NSERC (Canada) [255307]
- National Natural Science Foundation of China [11871017]
- China Postdoctoral Science Foundation [2013M540270]
- Fundamental Research Funds for the Central Universities, China
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This paper deals with blow-up of positive solutions for a singular Gierer-Meinhardt system subject to zero Dirichlet boundary conditions. We first prove the existence of a local solution and then show blow-up solutions under certain conditions for parameters. We use a functional method to obtain a local solution which is bounded by the first eigenfunction both from above and from below and then obtain the bound of a ratio of two solutions. This method is completely different from the traditional methods of sub and super solutions. (C) 2019 Elsevier Ltd. All rights reserved.
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