Identification of memory kernels in general linear heat flow

Journal of Inverse and Ill-Posed Problems

Volumn 6, Issue 2, 1998, Pages 141-164

  Janno, J ^a   Wolfersdorf, L V ^b  

^a Institute of Cybernetics   (United Kingdom)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346483265     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/jiip.1998.6.2.141     Document Type: Article

References (22)

1. J. Baumeister, Boundary control of an integrodifferential equation. J. Math. Anal. Appl (1983) 93, 550–570.
2. A. L. Bukhgeim, Inverse problems of memory reconstruction. J. Inv. Ill-Posed Problems (1993) 1, 193–205.
3. B. D. Coleman and M. E. Curtin, Equipresence and constitutive equation for rigid heat conductors. Z. Angew. Math. Phys. (1967) 18, 199–208.
4. P. L. Davis, On the hyperbolicity of the equations of the linear theory of heat conduction for materials with memory. SIAM J. Appl. Math. (1976) 30, 75–80.
5. G. Centili, Dissipativity conditions and inverse problems for heat conduction in materials with linear memory. Inverse Problems (1991) 7, 77–84.
6. H. Grambiiller, On linear theory of heat conduction in meterials with memory. Existence and uniqueness theorems for the final value problem. Proc. Royal Soc. Edinburgh. (1976) 76A, 119–137.
7. M. Crasselli, An identification problem for a linear integro-differential equation occuring in heat flow. Math. Meth. in Appl. Sci. (1992) 15, 167–186.
8. M. Crasselli and A. Lorentzi, An inverse problem fpr an abstract nonlinear parabolic integrodifferential equation. Diff. Int. Eqn. (1993) 6, 63–81.
9. M. E. Curtin and A. C. Pipkin, A general theory of heat conduction with finite speeds. Arch. Rational Mech. Anal. (1968) 31, 113–126.
10. J. Janno and L. V. Wolfersdorf, Inverse problems for identification of memory kernels in heat flow. J. Inv. Ill-Posed Problems (1996) 4, 39–66.
11. J. Janno and L. V. Wolfersdorf, Identification of weakly singular memory kernels in heat conduction. Z. Angew. Math. Mech. (to appear).
12. J. Janno and L. V. Wolfersdorf, On a class of multilinear operator equations. Z. Anal Anw. (1996) 15, 935–948.
13. A. Lorentzi, An inverse problem in the theory of materials with memory II. In: Semigroup Theory and Applications. Ser. Pure Appl. Math. 16, 261–290. M. Dekker, New York, 1989.
14. A. Lorentzi, Identification problems for integrodiiferential equations. In: Ill-Posed Problems in Natural Sciences (Ed. A Tikhonov), 342–366. TVP Sci. Publ., Moscow, 1992.
15. A. Lorentzi and Paparoni, Direct and inverse problems in the theory of materials with memory. Rend. Sem. Math. Univ. Padova (1992) 87, 105–138.
16. A. Lorentzi and E. Sinestrari, An inverse problems in the theory of materials with memory. Nonlin. Anal, Theory, Meth. and Appl (1988) 12, 1317–1335.
17. A. Lorentzi and E. Sinestrari, Stability results for a partial integrodifferential inverse problem. In: G.Da Prato and M. Janelli (Eds), Volterra equations in Banach spaces and applications, 271–294. Longman, Burnt Mill, Harlow, 1989.
18. A. Lunardi, On the linear equation with fading memory. SIAM J. Math. Anal. (1970) 21, 1213–1224.
19. J. Meixner, On the linear theory of heat conduction. Arch. Rat. Mech. Anal. (1970) 39, 108–130.
20. J. W. Nunziato, On heat equation in materials with memory. Quart. Appl Math. (1971) 29, 187–204.
21. J. Prüss, Evolutionary Integral Equations and Applications. Birkhäuser Verlag, Basel, 1993.
22. L. V. Wolfersdorf, On identification of memory kernels in linear theory of heat conduction. Math. Meth. in Appl. Sci. (1994) 17, 919–932.