Abstract
We study the behaviour of global solutions to the quasilinear heat equation with a reaction localizedut=(um)xx+a(x)up,m,p>0 and a(x) being the characteristic function of an interval. We prove that there exists an exponent p0=max{1,m+12} such that all global solutions are bounded if p>p0, while for p≤p0 all the solutions are global and unbounded. In the last case, we prove that if p<m the grow-up rate is different to the one obtained when a(x)≡1, while if p>m the grow-up rate coincides with that rate, but only inside the support of a; outside the interval the rate is smaller.
Published Version
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