FILTER REGULARIZATION FOR AN INVERSE PARABOLIC PROBLEM IN SEVERAL VARIABLES

被引：0

作者：

Tuan Nguyen Huy ^{[1
]}

Kirane, Mokhtar ^{[2
,3
]}

Le, Long Dinh ^{[4
]}

Thinh Van Nguyen ^{[5
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] Univ La Rochelle, Lab Math Pole Sci & Technol, F-17042 La Rochelle, France

[3] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia

[4] Inst Computat Sci & Technol, Ho Chi Minh City, Vietnam

[5] Seoul Natl Univ, Dept Civil & Environm Engn, Seoul 151, South Korea

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年

关键词：

Ill-posed problem; truncation method; heat equation; regularization; BOUNDARY-VALUE METHOD; BACKWARD; EQUATIONS; TIME; APPROXIMATION; STABILITY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The backward heat problem is known to be ill possed, which has lead to the design of several regularization methods. In this article we apply the method of filtering out the high frequencies from the data for a parabolic equation. First we identify two properties that if satisfied they imply the convergence of the approximate solution to the exact solution. Then we provide examples of filters that satisfy the two properties, and error estimates for their approximate solutions. We also provide numerical experiments to illustrate our results.

引用

页数：13

共 50 条

[41] AN INVERSE PROBLEM FOR A NONLINEAR PARABOLIC MODEL
Ciutureanu, Cornelia-Andreea
MATHEMATICAL REPORTS, 2011, 13 (01): : 1 - 13
[42] An Inverse Problem for a Parabolic Convolution Equation
Boumenir, A.
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2012, 55 (03): : 447 - 456
[43] INVERSE PROBLEM FOR AN EQUATION OF PARABOLIC TYPE
ROMANOV, VG
MATHEMATICAL NOTES, 1976, 19 (3-4) : 360 - 363
[44] A modified Tikhonov regularization method for a class of inverse parabolic problems
Saouli, Nabil
Zouyed, Fairouz
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2020, 28 (01): : 181 - 204
[45] New enzyme algorithm, Tikhonov regularization and inverse parabolic analysis
Yang, Xin-She
ADVANCES IN COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2005, VOLS 4 A & 4 B, 2005, 4A-4B : 1880 - 1883
[46] INVERSE PROBLEM FOR A PARABOLIC EQUATION AND A PROBLEM OF INTEGRAL GEOMETRY
KLIBANOV, MV
SIBERIAN MATHEMATICAL JOURNAL, 1976, 17 (03) : 435 - 440
[47] Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
Nguyen Duc Phuong
Le Dinh Long
Anh Tuan Nguyen
Baleanu, Dumitru
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2022, 38 (12) : 2199 - 2219
[48] Numerical Method for Solving an Inverse Boundary Problem with Unknown Initial Conditions for Parabolic PDE Using Discrete Regularization
Yaparova, Natalia M.
NUMERICAL ANALYSIS AND ITS APPLICATIONS (NAA 2016), 2017, 10187 : 752 - 759
[49] Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
Nguyen Duc PHUONG
Le Dinh LONG
Anh Tuan NGUYEN
Dumitru BALEANU
ActaMathematicaSinica,EnglishSeries, 2022, (12) : 2199 - 2219
[50] Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
Nguyen Duc Phuong
Le Dinh Long
Anh Tuan Nguyen
Dumitru Baleanu
Acta Mathematica Sinica, English Series, 2022, 38 : 2199 - 2219

← 1 2 3 4 5 →