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Resumen:
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This paper concerns the Cauchy problem ut?uxx=up, x?R, t>0, u(x,0)=u0(x), x?R, where p>1 and u0(x) is a continuous, nonnegative and bounded function. It has been previously proved that if x=x¯, t=T is a blow-up point, then there are three cases for the asymptotic behavior of a solution near the blow-up point. The main result of this paper is to prove that if u0?C+0(R), blow-up consists generically of a single point blow-up, with the behavior described in one case (case (b)). Moreover, the behavior is stable under small perturbations in the L?-norm of the initial value u0.
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