Abstract
This paper is concerned with the spreading properties for a reaction–diffusion equation in cylinder with partially exponentially unbounded initial condition u0(x,y). We prove that the level sets of the solutions move infinitely fast as time goes to infinity. We also prove that the locations of the level sets are determined by the maximum of the initial values with respect to y. Roughly speaking, our results imply that once the initial value u0(⋅,y) decays to zero, as x→∞, more slowly than any exponentially decaying function at one point y0∈Ω, then the level sets of the solutions of the equation will move infinitely fast as time goes to infinity.
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