Stability estimates in an inverse problem for a three-dimensional heat equation

SIAM Journal on Mathematical Analysis

Volumn 28, Issue 6, 1997, Pages 1354-1370

  Vessella, Sergio ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Inverse problem; Stability

Indexed keywords

EID: 0000267810     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095294262     Document Type: Article

References (14)

1. G. ALESSANDRINI, Stable determination of a crack from boundary measurements, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 497-516.
2. G. ALESSANDRINI, Stability for the crack determination problem, in Proc. Lapland Conference on Inverse Problems, Inari, 1992.
3. S. ANDRIEUX, A. BEN ABDA, AND M. JAOUA, Identifiabilitè de frontière inaccessible par des mesures de surface, C.R. Acad. Sci. Paris, 316 (1993), pp. 429-434.
4. A. BEN ABDA, Sur Quelques Problemes Inverses Geometriques via, des Equations de Conduction Elliptiques: Etude Theorique et Numerique, Ph.D. thesis, Ecole National d'ingenieurs de Tunis, 1993.
5. J. R. CANNON, The one dimensional heat equation, Addison-Wesley, Reading, MA, 1984.
6. A. ELAYYAN AND V. ISAKOV, On uniqueness of recovery of the discontinuos conductivity coefficient of a parabolic equation, SIAM J. Math. Anal., 28 (1997), pp. 49-59.
7. L. C. EVANS AND R. E. GARIEPY, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992.
8. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
9. A. FRIEDMAN AND M. VOGELIUS, Determining cracks by boundary measurements, Indiana Math. J., 38 (1989), pp. 527-556.
10. D. GILBARG AND N.S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin, New York, 1983.
11. A. GORNY, Contribution a l'étude des functions derivables d'une variable réelle, Acta Math., 71 (1939), pp. 317-358.
12. P. G. KAUP AND F. SANTOSA, Nondestructive evaluation of corrosion damage using electrostatic measurements, J. Nondestructive Eval., 1995.
13. M. M. LAVRENT'EV, V. G. ROMANOV, AND S. P. SHISHATSKII, Ill-posed problems of mathematical physics and analysis, Transi. Math. Monograph 64, Amer. Math. Soc., Providence, RI, 1986.
14. O. A. LADYZHENSKAJA, V. A. SOLONNIKOV, AND N. N. URAL'CEVA, Linear and quasilinear equations of parabolic type, Transl. Math. Monograph 23, Amer. Math. Soc., Providence, RI, 1968.