Global existence and blow-up of solutions to a nonlocal reaction-diffusion system

By Shuxiang Huang, Fucai Li, C. Xie. 2003

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This paper deals with a reaction-diffusion system with nonlocal sources. Under appropriate hypotheses, we obtain that the solution either exists globally or blows up in finite time by making use of super and sub solution techniques. In the situation when the solution blows up in finite time, we show that the blow-up set is the whole domain, which is quite different from the results with local sources. Furthermore, we obtain the blow-up rate of the solution.

Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/02a6a32a2b78768e0f3ebf4aab696123dfc139b0