Nonexistence results for a semilinear heat equation with bounded potentials. (March 2020) - Phan, Quoc Hung
Abstract: We study the Liouville type theorem for positive solutions to the semilinear heat equation u t − Δ u = V u p in R N × R . We show that the nonexistence of positive solutions holds for any p < 1 and for any V bounded from below by a positive constant. In the superlinear case p > 1, we give some sufficient conditions on the potential and the exponent which guarantee the nonexistence of positive solutions in the whole space.