Grow-up for a quasilinear heat equation with a localized reaction

2018/01/29 by Ferreira, Raul, de Pablo, Arturo
#35K55 #35K57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09525

Abstract

We study the behaviour of global solutions to the quasilinear heat equation with a reaction localized u_t=(u^m)_xx+a(x) u^p, m, p>0 and a(x) being the characteristic function of an interval. we prove that there exists p₀=max\1,\fracm+12\ such that all global solution are bounded if p>p₀, while for p≤ p₀ all the solution are global and unbounded. In the last case, we prove that if pm the grow-up rate coincides with that rate, but only inside the support of a; outside the interval the rate is smaller.

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