Determination of a coefficient in the wave equation with a single measurement

被引：32

作者：

Bellassoued, Mourad ^{[1
]}

Yamamoto, Masahiro ^{[2
]}

机构：

[1] Univ Carthage, Fac Sci Bizerte, Dept Math, Bizerte, Tunisia

[2] Univ Tokyo, Dept Math Sci, Tokyo, Japan

来源：

APPLICABLE ANALYSIS | 2008年 / 87卷 / 08期

关键词：

Carleman estimates; inverse problems;

D O I：

10.1080/00036810802369249

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an inverse problem of finding the coefficient of the second-order derivatives in a second-order hyperbolic equation with variable coefficients. Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement of Neumann data on a suitable sub-boundary. Moreover we show that our uniqueness yields the Lipschitz stability estimate in L(2) space for solution to the inverse problem. The key is a Carleman estimate for a hyperbolic operator with variable coefficients.

引用

页码：901 / 920

页数：20

共 23 条

[1]

Albano P., 2000, ELECTRON J DIFFER EQ, V22, P1

[2]

[Амиров A.X. Amirov A. Kh.], 2005, [Доклады Академии наук, Doklady Akademii nauk], V402, P7

[3]

Bellassoued M., 2004, APPL ANAL, V83, P983

[4]

BUGHEIM AL, 1981, SOV MATH DOKL, V24, P244

[5] An inverse problem for the dynamical Lame system with two sets of boundary data [J].

Imanuvilov, O ;

Isakov, V ;

Yamamoto, M .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2003, 56 (09) :1366-1382

[6]

Imanuvilov OU, 2001, COMMUN PART DIFF EQ, V26, P1409

[7]

Imanuvilov OY, 2002, ASYMPTOTIC ANAL, V32, P185

[8] Determination of a coefficient in an acoustic equation with a single measurement [J].

Imanuvilov, OY ;

Yamamoto, M .

INVERSE PROBLEMS, 2003, 19 (01) :157-171

[9] Global Lipschitz stability in an inverse hyperbolic problem by interior observations [J].

Imanuvilov, OY ;

Yamamoto, M .

INVERSE PROBLEMS, 2001, 17 (04) :717-728

[10]

ISAKOV V, 1998, INVERSE PROBLEMS PAR

← 1 2 3 →