Uniqueness and counterexamples in some inverse source problems

被引：6

作者：

Slodicka, M. ^{[1
]}

Johansson, B. Tomas ^{[2
]}

机构：

[1] Univ Ghent, Dept Math Anal, Res Grp Numer Anal & Math Modeling NaM2, Galglaan 2-S22, B-9000 Ghent, Belgium

[2] Aston Univ, Math, EAS, Birmingham B4 7ET, W Midlands, England

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 58卷

关键词：

Heat equation; Inverse source problem; DEPENDENT HEAT-SOURCE;

D O I：

10.1016/j.aml.2016.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：56 / 61

页数：6

共 50 条

[31] On Some Classes of Inverse Problems on Determining the Source Function
Pyatkov, S. G.
Safonov, E., I
PROCEEDINGS OF THE 8TH SCIENTIFIC CONFERENCE ON INFORMATION TECHNOLOGIES FOR INTELLIGENT DECISION MAKING SUPPORT (ITIDS 2020), 2020, 174 : 242 - 248
[32] Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations
Kostin, A. B.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2014, 54 (05) : 797 - 810
[33] UNIQUENESS THEOREMS OF SOME NONLINEAR INVERSE PROBLEMS OF PARABOLIC-TYPE EQUATIONS
LAVRENTE.MM
REZNITSK.KG
DOKLADY AKADEMII NAUK SSSR, 1973, 208 (03): : 531 - 532
[34] UNIQUENESS OF SOLUTION OF 2 INVERSE PROBLEMS
SHISHKO, NP
SIBERIAN MATHEMATICAL JOURNAL, 1975, 16 (02) : 309 - 313
[35] Uniqueness Theorems for Inverse Gravimetric Problems
Sampietro, D.
Sanso, F.
VII HOTINE-MARUSSI SYMPOSIUM ON MATHEMATICAL GEODESY, 2012, 137 : 111 - 115
[36] UNIQUENESS AND STABILITY IN MULTIDIMENSIONAL INVERSE PROBLEMS
ISAKOV, V
INVERSE PROBLEMS, 1993, 9 (06) : 579 - 621
[37] UNIQUENESS FOR INVERSE ELASTIC MEDIUM PROBLEMS
Barcelo, J. A.
Folch-Gabayet, M.
Perez-Esteva, S.
Ruiz, A.
Vilela, M. C.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2018, 50 (04) : 3939 - 3962
[38] Holder stability estimates for some inverse pointwise source problems
El Badia, Abdellatif
El Hajj, Ahmad
COMPTES RENDUS MATHEMATIQUE, 2012, 350 (23-24) : 1031 - 1035
[39] UNIQUENESS THEOREMS FOR INVERSE PROBLEMS RELATED TO SOME 2ND-ORDER EQUATIONS
ROMANOV, VG
DOKLADY AKADEMII NAUK SSSR, 1991, 321 (02): : 254 - 257
[40] Uniqueness of an inverse source problem in experimental aeroacoustics
Hohage, Thorsten
Raumer, Hans-Georg
Spehr, Carsten
INVERSE PROBLEMS, 2020, 36 (07)

← 1 2 3 4 5 →