Abstract
This paper examines the existence, structure and bifurcation (in the parameters N and p ) of a class of global positive similarity solutions to the semilinear parabolic equation u t = ∇ N 2 u + u p , with p > 1 and N ⩾ 1. Here ∇ N 2 is the N –dimensional Laplace operator. These are related to the existence of‘geometric threshold’ in the p th–order autocatalytic or chain–branching reactions.
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