具有初始基准的热方程下资料同化的稳定性估计

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI:10.5802/crmath.506

Erik Burman, Guillaume Delay, Alexandre Ern, Lauri Oksanen

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引用次数: 0

摘要

本文研究了热方程的唯一延拓问题。我们证明了解的条件稳定性估计。我们感兴趣的是Hölder稳定的局部估计，右边的数据可能是最弱的规范。这种估计对处理数据同化的计算方法的收敛性分析是有用的。我们主要讨论在初始时间和某一子域上解已知，但在边界上解未知的情况。据我们所知，这种情况还没有在文献中研究过。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A stability estimate for data assimilation subject to the heat equation with initial datum

This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for the convergence analysis of computational methods dealing with data assimilation. We focus on the case of a known solution at initial time and in some subdomain but that is unknown on the boundary. To the best of our knowledge, this situation has not yet been studied in the literature.

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.