Inverse problems for identification of memory kernels in viscoelasticity

Mathematical Methods in the Applied Sciences

Volumn 20, Issue 4, 1997, Pages 291-314

  Janno, J ^a,b   Von Wolfersdorf, L ^b  

^a TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; INVERSE PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

CONTRACTION PRINCIPLE; MEMORY KERNELS; VOLTERRA INTEGRAL EQUATIONS;

VISCOELASTICITY;

EID: 0031102982     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19970310)20:4<291::AID-MMA860>3.0.CO;2-W     Document Type: Article

References (26)

1. Bukhgeim, A. L., 'Inverse problems of memory reconstruction', J. Inverse III-Posed Problems, 1, 193-205 (1993).
2. Cavaterra, C. and Grasselli, M., 'An inverse problem for the linear viscoelastic Kirchhoff plate', Quart. Appl. Math., 53, 9-33 (1995).
3. Cavaterra, C. and Grasselli, M., 'On an inverse problem for a model of linear viscoelastic Kirchhoff plate', submitted.
4. Grasselli, M., 'An identification problem for an abstract linear hyperbolic integrodifferential equation with applications', J. Math. Anal. Appl., 171, 27-60 (1992).
5. Grasselli, M.: 'Determining the relaxation tensor in linear viscoelasticity of integral type', Japan J. Ind. Appl. Math., 11, 131-153 (1994).
6. Grasselli, M., 'On an inverse problem for a linear hyperbolic integrodifferential equation', Forum Math., 6, 83-100 (1994).
7. Grasselli, M., 'Identifying relaxation kernels of linearly viscoelastic bodies', submitted.
8. Grasselli, M., Kabanikhin, S. I. and Lorenzi A., 'An inverse hyperbolic integrodifferential problem arising in geophysics I', Sibirsk. Mat. Zh., 33, 58-68 (1992) (in Russian).
9. Grasselli, M., Kabanikhin, S. I. and Lorenzi, A., 'An inverse hyperbolic integrodifferential problem arising in geophysics II', Nonlin. Anal., Theory, Methods Appl., 15, 283-298 (1990).
10. Janno, J., 'On an inverse problem for a hyperbolic equation', Uch. Zap. Tartu Gos. Univ., 672, 40-46 (1984).
11. Janno, J., 'On an inverse problem for a model of radially wave propagation in the media with memory', in: Numerical Methods and Optimization, Vol. 2 (eds., G. Vainikko et al), Eston. Acad. Sci., Tallinn 1990, pp. 4-19.
12. Janno, J., 'On an inverse problem for determining the creep function with a given boundary data close to a singular function', Intern. Ser. Numer. Math., 100, 187-195 (1991).
13. Janno, J., 'On a well-posed approximation of an inverse problem in isotropic medium with memory', Numer. Funct. Anal. Optim., 13, 277-286 (1992).
14. Janno, J., 'Global existence for a hyperbolic integrodifferential inverse problem', Forum Math., to appear.
15. Janno, J., 'An inverse problem for a quasilinear integrodifferential wave equation', Proc. Eston. Acad. Sci. Phys. Math. 45, 1-22 (1996).
16. Janno, J. and Von Wolfersdorf, L., 'Inverse problems for identification of memory kernels in heat flow', J. Inv. Ill-Posed Problems, 4, 39-66 (1996).
17. Janno, J. and Von Wolfersdorf, L., 'Identification of weakly singular memory kernels in heat conduction', Z. Angew. Math. Mech., to appear.
18. Kabanikhin, S. I., Karchevsky, A. L. and Lorenzi, A., 'Lavrent'ev regularization of solutions to linear integrodifferential inverse problems', J. Inv. Ill-Posed Problems, 1, 115-140 (1993).
19. Lorenzi, A., 'Identification problems for integrodifferential equations', in: Ill-Posed Problems in Natural Sciences (ed. A. Tikhonov), TVP Sci. Publ., Moscow, 1992, pp. 342-366.
20. Lorenzi, A., 'An identification problem related to a nonlinear hyperbolic integrodifferential equation', Nonlin. Anal., Theory, Meth. Appl, 22, 21-44 (1994).
21. Lorenzi, A., 'Regularization of hyperbolic integrodifferential identification problems', J. Inv. Ill-Posed Problems, 2, 291-321 (1994).
22. Lorenzi, A., Ulenkova, J. Sh, and Yakhno, V. G., 'An inverse problem in viscoelasticity', J. Inv. Ill-Posed Problems, 2, 131-165 (1994).
23. Renardy, M., Hrusa, W. J. and Nohel, J. A., Mathematical Problems in Viscoelasticity, Longman, Burnt Mill, Harlow, 1987.
24. Tobias, T. A., Engelbrecht, J. K., 'On inverse problems for evolution equations of integrodifferential type', Prikl. Mat. Mekh., 49, 676-682 (1985) (in Russian).
25. Von Wolfersdorf, L., 'On identification of memory kernels in linear viscoelasticity', Math. Nachrichten 161, 203-217 (1993).
26. Von Wolfersdorf, L., 'On optimality conditions in some control problems for memory kernels in viscoelasticity', Z. Anal. Anwend., 12, 745-750 (1993).