Spatial asymptotics and equilibria of heat flow on ℝ^d

2019/12/16 by McOwen, Robert, Topalov, Peter
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.07707

Abstract

We prove that the heat equation on ℝ^d is well-posed in certain spaces of functions allowing spatial asymptotic expansions as |x|→∞ of any a priori given order. In fact, we show that the Laplacian on such function spaces generates an analytic semigroup of angle π/2 with polynomial growth as t→∞. Generically, a large class of nonlinear heat flows have equilibrium solutions with spatial asymptotics of the considered type. We provide a simple nonlinear model that features global in time existence with such asymptotics at spatial infinity.

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