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• W3100708605 abstract "We prove a global approximation theorem for a general parabolic operator $L$, which asserts that if $v$ satisfies the equation $Lv=0$ in a spacetime region $Omega subset mathbb{R}^{n+1}$ satisfying certain necessary topological condition, then it can be approximated in a Holder norm by a global solution $u$ to the equation. If $Omega$ is compact and $L$ is the usual heat operator, one can instead approximate the local solution $v$ by the unique solution that falls off at infinity to the Cauchy problem with a suitably chosen smooth, compactly supported initial datum. These results are next applied to prove the existence of global solutions to the equation $Lu=0$ with a local hot spot that moves along a prescribed curve for all time, up to a uniformly small error. Global solutions that exhibit isothermic hypersurfaces of prescribed topologies for all times and applications to the heat equation on the flat torus are discussed too." @default.
• W3100708605 created "2020-11-23" @default.
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• W3100708605 date "2019-04-01" @default.
• W3100708605 modified "2023-10-18" @default.
• W3100708605 title "Approximation theorems for parabolic equations and movement of local hot spots" @default.
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• W3100708605 doi "https://doi.org/10.1215/00127094-2018-0058" @default.
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