Geodesic
On a reliable solution of a Volterra integral equation in a Hilbert space
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 469-486.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to a quasistationary problem for an anisotropic viscoelastic body made of a long memory material.
DOI : 10.1023/B:APOM.0000024487.48855.d9
Classification : 45D05, 45N05, 49J22, 65R20, 74D05
Keywords: Volterra integral equation in a Hilbert space; Rothe’s method; maximization problem; viscoelastic body 
@article{10_1023_B_APOM_0000024487_48855_d9,
     author = {Bock, Igor and Lov{\'\i}\v{s}ek, J\'an},
     title = {On a reliable solution of a {Volterra} integral equation in a {Hilbert} space},
     journal = {Applications of Mathematics},
     pages = {469--486},
     publisher = {mathdoc},
     volume = {48},
     number = {6},
     year = {2003},
     doi = {10.1023/B:APOM.0000024487.48855.d9},
     mrnumber = {2025957},
     zbl = {1099.45001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024487.48855.d9/}
}
TY  - JOUR
AU  - Bock, Igor
AU  - Lovíšek, Ján
TI  - On a reliable solution of a Volterra integral equation in a Hilbert space
JO  - Applications of Mathematics
PY  - 2003
SP  - 469
EP  - 486
VL  - 48
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024487.48855.d9/
DO  - 10.1023/B:APOM.0000024487.48855.d9
LA  - en
ID  - 10_1023_B_APOM_0000024487_48855_d9
ER  - 
%0 Journal Article
%A Bock, Igor
%A Lovíšek, Ján
%T On a reliable solution of a Volterra integral equation in a Hilbert space
%J Applications of Mathematics
%D 2003
%P 469-486
%V 48
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024487.48855.d9/
%R 10.1023/B:APOM.0000024487.48855.d9
%G en
%F 10_1023_B_APOM_0000024487_48855_d9
Bock, Igor; Lovíšek, Ján. On a reliable solution of a Volterra integral equation in a Hilbert space. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 469-486. doi : 10.1023/B:APOM.0000024487.48855.d9. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024487.48855.d9/

Cité par Sources :