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