Non-simultaneous blow-up for a semilinear parabolic system with nonlinear memory
Journal Title: Surveys in Mathematics and its Applications - Year 2007, Vol 2, Issue 0
Abstract
In this note, we study the possibility of non-simultaneous blow-up for positive solutions to the following system:<BR>u<sub>t</sub> - ∆u = u<sup>q<sub>1</sub></sup>∫<sub>0</sub><sup>t</sup> v<sup>p<sub>1</sub></sup>(x,s) ds, v<sub>t</sub> - ∆v = v<sup>q<sub>2</sub></sup>∫<sub>0</sub><sup>t</sup> u<sup>p<sub>2</sub></sup>(x,s) ds <BR>Under appropriate hypotheses, we prove that u blows up while v fails to blow up if and only if q<sub>1</sub> > 1 and p<sub>2</sub> < 2q<sub>1</sub>-1).
Authors and Affiliations
Jun Zhou
Keywords
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