Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations

机译：数值求解抛物线方程中最低阶空间明智系数的迭代过程

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In this work we suggest an iterative process for coefficient inverse problem. A parabolic equation in a bounded area supplied with initial condition and monotonic nondecreasing on time Dirichlet condition on a boundary is considered. We state a problem to recover the lowest order coefficient that depends only on spatial variables under an additional information as the observation of a solution taken at the final point of time. For numerical recovering of the coefficient we build the iterative process, at each iteration we perform finite-element approximation in space and fully implicit two-level discretization in time. For capabilities of given iterative process we present computational test for a model problem.

机译：在这项工作中，我们提出了系数反问题的迭代过程。考虑边界条件下抛物线方程的边界条件，该抛物线方程具有初始条件并且在时间上具有单调非递减Dirichlet条件。我们提出了一个问题，那就是要恢复仅依赖于空间变量的最低阶系数，这是在最后时刻观察到的解决方案的附加信息。为了对系数进行数值恢复，我们建立了迭代过程，在每次迭代中，我们在空间中执行有限元逼近，并在时间上执行完全隐式两级离散化。对于给定迭代过程的功能，我们提出了模型问题的计算测试。

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来源
《Finite difference methods: theory and applications》|2018年|289-296|共8页
会议地点 Lozenetz(BG)
作者
D. Kh. Ivanov; P. N. Vabishchevich;
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作者单位

Institute of Mathematics and Information Science, North-Eastern Federal University, 58, Belinskogo, Yakutsk, Russia;

Institute of Mathematics and Information Science, North-Eastern Federal University, 58, Belinskogo, Yakutsk, Russia,Nuclear Safety Institute, Russian Academy of Sciences, 52, B. Tulskaya, Moscow, Russia;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Inverse problem; Parabolic equation; Finite element method; Implicit scheme;

机译：反问题；抛物线方程有限元法；隐式方案;

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专利

1. Computational identification of the lowest space-wise dependent coefficient of a parabolic equation [J] . Petr N. Vabishchevich Applied Mathematical Modelling . 2019,第JANa期

机译：抛物线方程最低与空间相关的系数的计算识别
2. NUMERICAL PROCEDURES FOR RECOVERING A TIME DEPENDENT COEFFICIENT IN A PARABOLIC DIFFERENTIAL EQUATION [J] . Hossein Azari, Walter Allegretto, Yanping Lin, Dynamics of continuous, discrete & impulsive systems, Series B. Applications & algorithms . 2004,第1a2期

机译：抛物面微分方程中恢复时间相关系数的数值过程
3. The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables [J] . V. L. Kamynin Mathematical notes . 2015,第3a4期

机译：同时确定具有多个空间变量的抛物线方程中右侧和最低系数的反问题
4. Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations [C] . D. Kh. Ivanov, P. N. Vabishchevich International Conference on Finite Difference Methods . 2019

机译：抛物线方程中最低阶空间系数数值恢复的迭代过程
5. Numerical identification of transmissivity coefficients in elliptic and parabolic equations by mollification techniques [D] . Hinestroza Gutierrez, Doris 1992

机译：椭圆和抛物线方程透射系数的变小技术数值识别。
6. PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH TIME DEPENDENT COEFFICIENTS [O] . 1957

机译：具有时间相关系数的微分方程的抛物线方程组
7. Computational identification of the lowest space-wise dependent coefficient of a parabolic equation [O] . Petr N. Vabishchevich 2019

机译：抛物线方程最低空洞依赖系数的计算识别
8. Optimal Processes Described by a Parabolic Differential Equation with Control in the Coefficients, Part 3 [R] . Vanmarle, E. A., Nottrot, R. 1988

机译：由系数控制的抛物型微分方程描述的最优过程，第3部分

Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations

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