In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation uₜ = \Δ u + uᵖ in RN with $p > 1$ and nonnegative initial values. Fujita showed that if 1 < p < 1 + 2 / N, then the initial value problem had no nontrivial global solutions while if p > 1 + 2 / N, there were nontrivial global solutions. This paper discusses similar results for other geometries and other equations including a nonlinear wave equation and a nonlinear Schrödinger equation.
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Howard A. Levine (1990) studied this question.
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