STABILITY OF THE DETERMINATION OF A TIME-DEPENDENT COEFFICIENT IN PARABOLIC EQUATIONS

被引：20

作者：

Choulli, Mourad ^{[1
]}

Kian, Yavar ^{[2
]}

机构：

[1] Univ Lorraine, LMAM, UMR 7122, F-57045 Metz 1, France

[2] Aix Marseille Univ, UMR 7332, Ctr Phys Theor, F-13288 Marseille 9, France

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2013年 / 3卷 / 02期

关键词：

Parabolic equation; semi-linear parabolic equation; inverse problem; determination of time-depend coefficient; stability estimate; INVERSE PROBLEM; HEAT-EQUATION; PARAMETER;

D O I：

10.3934/mcrf.2013.3.143

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient sigma(t), appearing in a Dirichlet initial-boundary value problem for the parabolic equation partial derivative(t)u - Delta(x)u + sigma (t) integral (x) u = 0, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation is changed to the semi-linear parabolic equation partial derivative(t)u - Delta(x)u = F(x, t,sigma (t); u(x; t)).

引用

页码：143 / 160

页数：18

共 19 条

[1]

[Anonymous], 1968, Amer. Math. Soc., Transl. Math. Monographs

[2]

Cannon J. R., 1986, INT SCHRIFTENREIHE N, V77, P133

[3] AN INVERSE PROBLEM OF FINDING A PARAMETER IN A SEMILINEAR HEAT-EQUATION [J].

CANNON, JR ;

LIN, YP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1990, 145 (02) :470-484

[4] DETERMINATION OF A PARAMETER P(T) IN SOME QUASI-LINEAR PARABOLIC DIFFERENTIAL-EQUATIONS [J].

CANNON, JR ;

LIN, YP .

INVERSE PROBLEMS, 1988, 4 (01) :35-45

[5] AN INVERSE PROBLEM FOR THE HEAT-EQUATION [J].

CANNON, JR ;

ESTEVA, SP .

INVERSE PROBLEMS, 1986, 2 (04) :395-403

[6] Stable determination of a semilinear term in a parabolic equation [J].

Choulli, M ;

Ouhabaz, EM ;

Yamamoto, M .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (03) :447-462

[7] ABSTRACT INVERSE PROBLEM AND APPLICATION [J].

CHOULLI, M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 160 (01) :190-202

[8]

Choulli M., 2009, MATH APPL BERLIN, V65

[9]

Choulli M., 1991, J APPL MATH STOC ANA, V4, P117

[10]

CHOULLI M., 2006, J. Inverse Ill-Posed Probl., V14, P355

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