Acta mathematica scientia, Series B >
INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES
Received date: 2009-09-25
Online published: 2011-07-20
Supported by
Project supported by the NSFC (10971019); Scientific Research Fund of Guangxi Education Department (201012MS067); and USM Grant No.12.09.05.
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gra-dient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.
LIU Zhen-Hai , I.Szántò . INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1318 -1326 . DOI: 10.1016/S0252-9602(11)60318-4
[1] Clarke F H. Optimization and Nonsmooth Analysis. Philadelphia: SIAM, 1990
[2] Hasanov A, Liu Zhenhai. An inverse coefficient problem for a nonlinear parabolic variational inequality. Appl Math Lett, 2008 21(6): 563–570
[3] Kohn R, Vogelius M. Determining conductivity by boundary measurements. Commun Pure Appl Math, 1984, 37: 289–298
[4] Ladyzhenskaya O A. Boundary Value Problems in Mathematical Physics. New York: Springer, 1985
[5] Liu Zhenhai. On the identification of coefficients of semilinear parabolic equations. Acta Math Appl Sinica, 1994, 10: 356–367
[6] Liu Zhenhai. Identification of parameters in semilinear parabolic equations. Acta Mathematica Scientia, 1999, 19: 175–180
[7] Liu Zhenhai. A class of evolution hemivariational inequalities. Nonlinear Analysis, 1999, 36: 91–100
[8] Liu Zhenhai. Generalized quasi-variational hemivariational inequalities. Appl Math Lett, 2004, 17: 741–745
[9] Liu Zhenhai. Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities. In-verse Problems, 2005, 21: 13–20
[10] Liu Zhenhai. Existence results for quasilinear parabolic hemivariational inequalities. J Differ Equ, 2008, 244: 1395–1409
[11] Liu Zhenhai, Wang B Y. Coefficient identification in parabolic equations. Appl Math Compn, 2009, 209: 379–390
[12] Tikhonov A, Arsenin V. Solutions of Ill-Posed problems. New York: Wiley 1977
[13] Zeidler E. Nonlinear Functional Analysis and Its Applications II A/B. New York: Springer, 1990
[14] Chen H F. Recursive system identification. Acta Mathematica Scientia, 2009, 29B(3): 650–672
[15] Xu Y J, Liu Zhenhai. Controllability for a parabolic equation with a nonlinear term involving the state and the gradient. Acta Mathematica Scientia, 2010, 30B(5): 1593–1604
/
| 〈 |
|
〉 |