Multiple blow-up for a porous medium equation with reaction
نویسندگان
چکیده
The present paper is concerned with the Cauchy problem { ∂tu = ∆u + u in R × (0,∞), u(x, 0) = u0(x) ≥ 0 in R , with p,m > 1. A solution u with bounded initial data is said to blow up at a finite time T if lim supt↗T ‖u(t)‖L∞(RN ) = ∞. For N ≥ 3 we obtain, in a certain range of values of p, weak solutions which blow up at several times and become bounded in intervals between these blow-up times. We also prove a result of a more technical nature: proper solutions are weak solutions up to the complete blow-up time.
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