Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-03-31 DOI:10.1515/jiip-2022-0030

K. Cao

引用次数: 0

Abstract

Abstract The determination of an unknown time-dependent source term is investigated in a Kuramoto–Sivashinsky equation from given additional integral-type measurement. Based on Schauder’s fixed point theorem, the existence and uniqueness of such inverse problem are obtained under certain assumptions on the input data. In order to calculate the unknown source term, a time-discrete system is established, and its solution shall be applied to approximate the unknown quantity. The existence, uniqueness and some estimates to the time-discrete system are derived, and the convergence rates are deduced rigorously for both exact and noisy observation, respectively. Finally, the theoretical convergence rate results are verified, and accurate and stable solutions to the inverse problem are computed numerically by two numerical experiments.

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Kuramoto–Sivashinsky方程中时间依赖源项的识别

摘要在Kuramoto–Sivashinsky方程中，通过给定的附加积分型测量，研究了未知时间依赖源项的确定。基于Schauder不动点定理，在输入数据的一定假设下，得到了这类逆问题的存在性和唯一性。为了计算未知源项，建立了一个时间离散系统，并应用其解来近似未知量。导出了时间离散系统的存在性、唯一性和一些估计，并分别对精确观测和噪声观测严格推导了收敛速度。最后，验证了理论收敛速度的结果，并通过两个数值实验对反问题的精确稳定解进行了数值计算。

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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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography