Remarks on A 2-D nonlinear backward heat problem using a truncated fourier series method

Electronic Journal of Differential Equations

Volumn 2009, Issue , 2009, Pages 1-13

  Trong, Dang Duc ^a   Tuan, Nguyen Huy ^b  

^a VIETNAM NATIONAL UNIVERSITY   (Viet Nam)

^b TON DUC THANG UNIVERSITY   (Viet Nam)

Author keywords

Backward heat problem; Contraction principle; Fourier series; Nonlinearly ill posed problem

Indexed keywords

EID: 68249112942     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. S. M. Alekseeva and N. I Yurchuk; The quasi-reversibility method for the problem of the control of an initial condition for the heat equation with an integral boundary condition, Differential Equations 34, no. 4, 493-500, 1998.
2. K. A. Ames and L. E. Payne; Continuous dependence on modeling for some well-posed perturbations of the backward heat equation, J. Inequal. Appl. 3, no 1, 51-64, 1999.
3. K. A. Ames, L. E. Payne; Continuous dependence on modeling for some well-posed perturbations of the backward heat equation, J. Inequal. Appl., Vol. 3 (1999), 51-64. ddtrong@math.hcmuns.edu.vn tuanhuy-bs@yahoo.com HoChiMinh City National University, Department of Mathematics and Informatics, 227 Nguyen Van Cu, Q. 5, HoChiMinh City, Vietnam Department of Information Technology and Applied Mathematics Ton Duc Thang University 98 Ngo Tat To, Hochiminh City, Vietnam
4. K. A. Ames, R. J. Hughes; Structural Stability for Ill-Posed Problems in Banach Space, Semigroup Forum, Vol. 70 (2005), no 1, 127-145.
5. G. W. Clark, S. F. Oppenheimer; Quasireversibility methods for non-well posed problems, Electron. J. Diff. Eqns., 1994 (1994) no. 8, 1-9.
6. M. Denche and K. Bessila; Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition , Math. Probl. Eng. 7, no 2, 129-145, 2001.
7. M. Denche and K. Bessila; A modified quasi-boundary value method for ill-posed problems, J. Math. Anal. Appl, Vol. 301, 2005, pp. 419-426.
8. R. E. Ewing; The approximation of certain parabolic equations backward in time by Sobolev equations, SIAM J. Math. Anal., Vol. 6 (1975), No. 2, 283-294.
9. H. Gajewski, K. Zaccharias; Zur regularisierung einer klass nichtkorrekter probleme bei evolutiongleichungen, J. Math. Anal. Appl., Vol. 38 (1972), 784-789.
10. Y. Huang, Q. Zhneg; Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups, J. Differential Equations, Vol. 203 (2004), No. 1, 38-54.
11. Y. Huang, Q. Zhneg; Regularization for a class of ill-posed Cauchy problems, Proc. Amer. Math. Soc. 133 (2005), 3005-3012.
12. R. Lattès, J.-L. Lions; Methode de Quasi- réversibilité et Applications, Dunod, Paris, 1967.
13. N. T. Long, A. P. Ngoc Ding; Approximation of a parabolic non-linear evolution equation backwards in time, Inv. Problems, 10 (1994), 905-914.
14. K. Miller; Stabilized quasi-reversibility and other nearly-best-possible methods for non-well posed problems, Symposium on Non-Well Posed Problems and Logarithmic Convexity, Lecture Notes in Mathematics, 316 (1973), Springer-Verlag, Berlin , 161-176.
15. P. H. Quan and D. D. Trong; A nonlinearly backward heat problem,: uniqueness, regularization and error estimate, Applicable Analysis, Vol. 85, Nos. 6-7, June-July 2006, pp. 641-657.
16. R. E. Showalter; The final value problem for evoluttion equations, J. Math. Anal. Appl, 47 (1974), 563-572.
17. R. E. Showalter; Cauchy problem for hyper-parabolic partial differential equations, in Trends in the Theory and Practice of Non-Linear Analysis, Elsevier 1983.
18. R. E. Showalter; Quasi-reversibility of first and second order parabolic evolution equations, Improperly posed boundary value problems (Conf., Univ. New Mexico, Albuquerque, N. M., 1974), pp. 76-84. Res. Notes in Math., no 1, Pitman, London, 1975.
19. D. D. Trong and N. H. Tuan; Regularization and error estimates for nonhomogeneous backward heat problems, Electron. J. Diff. Eqns., Vol. 2006 , No. 04, 2006, pp. 1-10.
20. D. D. Trong, P. H. Quan, T. V. Khanh, and N. H. Tuan; A nonlinear case of the 1-D backward heat problem: Regularization and error estimate, Zeitschrift Analysis und ihre Anwendungen, Volume 26, Issue 2, 2007, pp. 231-245.
21. D. D. Trong and N. H. Tuan; A nonhomogeneous backward heat problem: Regularization and error estimates , Electron. J. Diff. Eqns., Vol. 2008 , No. 33, pp. 1-14.
22. D. D. Trong and N. H. Tuan; Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems , Electron. J. Diff. Eqns., Vol. 2008 , No. 84, pp. 1-12.