Abstract
The present paper is concerned with the Cauchy problem
with p, m > 1. A solution u with bounded initial data is said to blow up at a finite time T if \({{\lim {\rm sup}_{t \nearrow T}||u(t)||_{L^\infty(\mathbb{R}^N)} =\infty}}\). 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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Mizoguchi, N., Quirós, F. & Vázquez, J.L. Multiple blow-up for a porous medium equation with reaction. Math. Ann. 350, 801–827 (2011). https://doi.org/10.1007/s00208-010-0584-5
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DOI: https://doi.org/10.1007/s00208-010-0584-5