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A Blow-up Dichotomy for Semilinear Fractional Heat Equations (1912.01537v1)
Published 3 Dec 2019 in math.AP
Abstract: We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.