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THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS
Lin Zhigui, Xie Chunhong, Wang Mingxin
Acta mathematica scientia,Series B. 1998, 18 (4):
413-420.
This paper deals with the blow-up properties of solutions to the systems ut △u=ev(x0,t), vt-△v=ev(x0,t) in Ω×(0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.
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