Global existence of solutions of a semilinear heat equation with nonlinear memory condition

We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow-up in finite time of all nontrivial solutions. The results depend on the behavior of variable coefficients as t → ∞. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.