Blow-up phenomena for <Emphasis Type="Italic">p</Emphasis>-adic semilinear heat equations

The problem of existence of solutions to p-adic semilinear heat equations with particular nonlinear terms has already been studied in the literature but the occurrence of blow-up phenomena has not been considered yet. We initiate the study of finite time blow-up for solutions of this kind of p-adic semilinear equations, proving that this phenomenon always arises under appropriate assumptions in the case when the exponent of nonlinearity times the dimension is strictly less than the order of the operator.