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Inverse coefficient problems for nonlinear elliptic equations

Published online by Cambridge University Press:  17 February 2009

Runsheng Yang  and
Yunhua Ou
Runsheng Yang
Affiliation:
department of Mathematics, Changsha University of Sciences and Technology Changsha Hunan 410076 P. R. Chin;email: runshengyang@126.com.
Yunhua Ou
Affiliation:
department of Mathematics, Hunan University of Technology Zhuzhou Hunan 412007 P. R. China; email: yunhuaou01@126.com.
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Abstract

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This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic equations. The unknown coefficient of the elliptic equations depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic equations are uniquely solvable for the given class of coefficients. Proof of the existence of a quasisolution of the inverse problems is obtained.

Keywords

elliptic equationsinverse coefficient problemsexistence of quasisolutions.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 271 - 279
Copyright
Copyright © Australian Mathematical Society 2007

References

[1] Cannon, J. R. and DuChateau, P. C., “Determination of the conductivity of an isotropic medium”, J Math Anal Appl 48 (1974) 699–707.CrossRefGoogle Scholar
[2] Cannon, J. R. and Rundell, W., “An inverse problem for an elliptic partial differential equation”, J Math Anal Appl 126 (1987) 329–340.CrossRefGoogle Scholar
[3] Hasanov, A., “An inverse coefficient problem for an elasto–plastic medium”, SIAM J Appl Math 55(1995)1736–1752.CrossRefGoogle Scholar
[4] Hasanov, A., “Inverse coefficient problems for monotone potential operators”, Inverse Problems 13 (1997) 1265–1278.CrossRefGoogle Scholar
[5] Hasanov, A., “Inverse coefficient problems for elliptic variational inequalities with a nonlinear operator”, Inverse Problems 14 (1998) 1251–1269.CrossRefGoogle Scholar
[6] Kohn, R. and Vogelius, M., “Determining conductivity by boundary measurements”, Commun Pure Appl Math 37 (1984) 289–298.CrossRefGoogle Scholar
[7] Ladyzhenskaya, O. A., Boundary value problems in mathematical physics (Springer, New York, 1985).CrossRefGoogle Scholar
[8] Liu, Zhenhai, “On the identification of coefficients of semilinear parabolic equations”, Ada Math Appl Sinica 10 (1994) 356–367.CrossRefGoogle Scholar
[9] Liu, Zhenhai, “A class of evolution hemivariational inequalities”, Nonlinear Anal 36 (1999) 91–100.Google Scholar
[10] Liu, Zhenhai, “Identification of parameters in semilinear parabolic equations”, Ada Math Sci 19 (1999) 175–180.Google Scholar
[11] Liu, Zhenhai, “Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities”, Inverse Problems 21 (2005) 13–20.CrossRefGoogle Scholar
[12] Liu, Zhenhai, “Strong convergence results for hemivariational inequalities”, Sci China Ser A 49 (2006)893–901.CrossRefGoogle Scholar
[13] Sylvester, J. and Uhlmann, G., “Inverse boundary value problems of the boundary-continuous dependence”, Commun Pure Appl Math 41 (1988) 197–219.CrossRefGoogle Scholar
[14] Tikhonov, A. and Arsenin, V., Solutions of ill-posed problems (Wiley, New York, 1977).Google Scholar
[15] Zeidler, E., Nonlinear functional analysis and its applications II A/B (Springer, New York, 1990).Google Scholar