紧黎曼流形上严格抛物方程的galerkin型方法

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-09-11 DOI:10.2422/2036-2145.202006_016

M. Graf, M. Kunzinger, Darko Mitrovich

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引用次数: 0

摘要

．证明了紧黎曼流形(M,g)上响应各种严格抛物型方程的柯西问题弱解的存在性。这也包括具有线性扩散的随机强迫的严格抛物方程。通过伽辽金方法的一种变体证明了其存在性，并可用于构造收敛有限元方法。

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Galerkin-type methods for strictly parabolic equations on compact Riemannian manifolds

. We prove existence of weak solutions to the Cauchy problem cor- responding to various strictly parabolic equations on a compact Riemannian manifold ( M,g ). This also includes strictly parabolic equations with stochas- tic forcing with linear diﬀusion. Existence is proved through a variant of the Galerkin method and can be used to construct a convergent ﬁnite element method.

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ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

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