An alternating method for an inverse Cauchy problem

1. V. Badeva and V. Morozov, Problèmes Incorrectement Posés. Théorie et Applications en Identi-fication, Filtrage Optimal, Contrôle Optimal, Analyse et Synthèse de Systèmes, Reconnaissance d'Images (Masson, Paris, 1991).

   Google Scholar 

2. A. Bakushinsky and A.V. Goncharsky, Ill-Posed Problems: Theory and Applications, Mathematics and Its Applications, Vol. 301 (Kluwer Academic, Dordrecht, 1994).

   Google Scholar 

3. C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques: Theory and Application in Engineering (Springer, Berlin, 1984).

   MATH  Google Scholar 

4. M. Costabel and E. Stephan, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, in: Mathematical Models and Methods in Mechanics, Banach Center Publications, Vol. 15 (Polish Acad. Sci., Warsaw, 1985) pp. 175–251.

   MATH  MathSciNet  Google Scholar 

5. J. Hayes and R. Kellner, The eigenvalue problem for a pair of coupled integral equations arising in the numerical solution of Laplace equation, SIAM. J. Appl. Math. 22(3) (1972) 503–513.

   Article  MATH  MathSciNet  Google Scholar 

6. J. Hess, Panel methods in computational fluid dynamics, Ann. Rev. Fluid Mech. 22 (1990) 255–274.

   Article  Google Scholar 

7. M. Jaswon and G. Symm, Integral Equation Methods in Potential Theory and Elastostatics (Academic Press, New York, 1977).

   MATH  Google Scholar 

8. M. Jourhmane and A. Nachaoui, A relaxation algorithm for solving a Cauchy problem, in: Proc. of the 2nd Internat. Conf. on Inverse Problems in Engineering, Engineering Foundation Editor, Vol. 1 (1996) pp. 151–158.

   Google Scholar 

9. M. Kobo, L2-conditional stability estimate for the Cauchy problem for the Laplace equation, J. Inv. Ill-Posed Problems 2(3) (1994) 253–261.

   Article  Google Scholar 

10. V.A. Kozlov, V.G. Maz'ya and A.V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations, Comput. Math. Phys. 31(1) (1991) 45–52.

    MATH  MathSciNet  Google Scholar 

11. M.M. Lavrentév, Some Ill-Posed Problems of Mathematical Physics (Izd. Sibirsk. Otd. Akad. Nauk SSSR, Novosibirsk, 1962).

    Google Scholar 

12. M.M. Lavrentév, V.G Romanov and V.G. Vasilév, Multidimensional Inverse Problems for Differential Equations (Izd. Sibirsk. Otd. Akad. Nauk SSSR, Novosibirsk, 1969).

    Google Scholar 

13. L.E. Payne, Bounds in the Cauchy problem for the Laplace equation, Arch. Rational Mech. Anal. 5 (1960) 35–45.

    Article  MATH  MathSciNet  Google Scholar 

14. L.E. Payne, Improperly Posed Problems in Partial Differential Equations, Regional Conference Series in Applied Mathematics, Vol. 22 (SIAM, Philadelphia, PA, 1975).

    MATH  Google Scholar 

15. A.N. Tikhonov and V.Ya. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

    Google Scholar 

16. A.N. Tikhonov and V.Ya. Arsenin, Methods for Solving Ill-Posed Preoblems (Nauka, Moscow, 1986).

    Google Scholar 

17. A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov and A.G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Mathematics and Its Applications, Vol. 328 (Kluwer Academic, Dordrecht, 1995).

    Google Scholar 

18. Y. Yamashita, Theoretical studies on the inverse problem in electrocardiography and the uniqueness of the solution, IEEE Trans. Biomed. Engrg. 29 (1982) 719–725.

    Google Scholar 

Download references