Abstract
We consider the nonlocal in time nonlinear heat equation
partial derivative(t)u - Delta u = 1/Gamma(1-gamma)integral(t)(0) (t-s)(-gamma)vertical bar u(s)vertical bar(p) ds + w(x), (t,x) is an element of (0,infinity) x D-c
with Dirichlet boundary conditions u(t, x) = f (t, x) >= 0, (t, x) is an element of (0, infinity) x partial derivative D, where D is the unit open ball in R-N, N >= 2, D-c is its complement, p > 1, 0 < gamma < 1 and w not equivalent to 0. We show that if u(0, .) >= 0 and integral D-c H (x)w(x) dx > 0, where H is a certain harmonic function on D-c, then for all p > 1, we have no global solutions. (C) 2019 Elsevier Ltd. All rights reserved.