Spatial asymptotics and equilibria of heat flow on $\mathbb{R}^d$

Robert McOwen; Peter Topalov

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arXiv · 1912.07707

Spatial asymptotics and equilibria of heat flow on $\mathbb{R}^d$

Robert McOwen·Peter Topalov

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Abstract

We prove that the heat equation on $\mathbb{R}^d$ is well-posed in certain spaces of functions allowing spatial asymptotic expansions as $|x|\to\infty$ of any a priori given order. In fact, we show that the Laplacian on such function spaces generates an analytic semigroup of angle $\pi/2$ with polynomial growth as $t\to\infty$. 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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Robert McOwen, Peter Topalov. 2019-12-16. Spatial asymptotics and equilibria of heat flow on $\mathbb{R}^d$. https://arxiv.org/abs/1912.07707

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