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Resumen:
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Consider the system (S) {ut–?u=v(p),inQ={(t,x),t>0, x??}, vt–?v=u(q), inQ, u(0,x)=u0(x)v(0,x)=v0(x)in?, u(t,x)=v(t,x)=0, whent?0, x???,
where ? is a bounded open domain in ?N with smooth boundary, p and q are positive parameters, and functions u0 (x), v0(x) are continuous, nonnegative and bounded. It is easy to show that (S) has a nonnegative classical solution defined in some cylinder QT=(0,T)×? with T||?. We prove here that solutions are actually unique if pq||1, or if one of the initial functions u0, v0 is different from zero when 01, solutions may be global or blow up in finite time, according to the size of the initial value (u0,v0).
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