Archive | 2021
A nonlinear diffusion equation with reaction localized in the half-line
Abstract
We study the behaviour of the solutions to the quasilinear heat equation with a reaction restricted to a half-line ut = (u )xx + a(x)u , m, p > 0 and a(x) = 1 for x > 0, a(x) = 0 for x < 0. We first characterize the global existence exponent p0 = 1 and the Fujita exponent pc = m + 2. Then we pass to study the grow-up rate in the case p ≤ 1 and the blow-up rate for p > 1. In particular we show that the grow-up rate is different as for global reaction if p > m or p = 1 6= m. In memoriam of our friend Ireneo Peral. Master of Mathematics