﻿ 带积分型源项二阶拋物型方程的参数识别问题 An Inverse Problem of Identifying the Coefficient of Second Order Parabolic Equation with Integral Source Term

Vol. 09  No. 03 ( 2020 ), Article ID: 34684 , 9 pages
10.12677/AAM.2020.93047

An Inverse Problem of Identifying the Coefficient of Second Order Parabolic Equation with Integral Source Term

Yujuan Zheng

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou Gansu

Received: Mar. 1st, 2020; accepted: Mar. 16th, 2020; published: Mar. 24th, 2020

ABSTRACT

This paper mainly studies an inverse problem of identifying the coefficient of second order parabolic equation with integral source term. We use the optimal control framework to establish control functional and prove the existence, and the necessary conditions of the minimum for the control functional are established. Since the optimal control problem is nonconvex, one may not expect a unique solution. However in this paper the solution is proved to be locally unique and stable.

Keywords:Inverse Problem, Optimal Control, Parameter Identification, Well-Posedness

1. 引言

(1.1)

(1.2)

(1.3)

(1.4)

2. 最优控制问题

(2.1)

(2.2)

(2.3)

(2.4)

3. 存在性

,

(3.1)

(3.2)

(3.3)

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4. 必要条件

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(4.2)

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(4.8)

(4.9)

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5. 局部唯一性和稳定性

(5.1)

(5.2)

(5.3)

(5.4)

(5.5)

(5.6)

C是T与无关的常数。

(5.7)

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(5.13)

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An Inverse Problem of Identifying the Coefficient of Second Order Parabolic Equation with Integral Source Term[J]. 应用数学进展, 2020, 09(03): 391-399. https://doi.org/10.12677/AAM.2020.93047

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