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where λ > 0. The function u(x, t) represents the dimensionless temperature when an electric current flows through a conductor (e.g. food) with temperature dependent on electrical resistivity f(u) > 0, subject to a fixed potential difference V > 0. The (dimensionless) resistivity f(u) may be either an increasing or a decreasing function of temperature depending strongly on the type of the material (food). Problem (1) models one of the main methods for sterilizing food. The sterilization can take place by electrically heating the food rapidly. Here λ is a dimensionless parameter and can be identified, amongst other things, with the square (being actually proportional) of the applied potential difference V. In the case where f(u) is a sufficiently rapidly decreasing function of temperature, there exists a critical value of the potential difference V, say V ∗, such that for V > V ∗ (equivalently

Blow-up time estimates for a non-local reactive-convective problem modelling sterilization of food