Geodesic
Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 118-134
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Cauchy problem for linear integro-differential operator equation with degenerated differential part of high order and convolutional type Volterra integral term is considered in article. Fundamental operator-function of integro-differential operator, appropriated of examining equation, is constructed, Cauchy problem generalized (in class of distributios with left-bounded support) and classical ($N$ times strongly continuously differentiable) solutions existence and uniqueness theorems are proved. Obtaining results are applied to the investigation of initial boundary value problems, arised in mathematical theory of elasticity.
Keywords: Banach space, Fredholm operator, fundamental operator-function.
Mots-clés : Jordan set, distribution 
@article{IIGUM_2011_4_1_a10,
     author = {M. V. Falaleev and S. S. Orlov},
     title = {Integro-differential equations with degeneration in {Banach} spaces and it's applications in mathematical theory of elasticity},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {118--134},
     year = {2011},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a10/}
}
TY  - JOUR
AU  - M. V. Falaleev
AU  - S. S. Orlov
TI  - Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2011
SP  - 118
EP  - 134
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a10/
LA  - ru
ID  - IIGUM_2011_4_1_a10
ER  - 
%0 Journal Article
%A M. V. Falaleev
%A S. S. Orlov
%T Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2011
%P 118-134
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a10/
%G ru
%F IIGUM_2011_4_1_a10
M. V. Falaleev; S. S. Orlov. Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 118-134. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a10/

[1] M. M. Vainberg, V. A. Trenogin, Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969, 528 pp. | MR

[2] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 320 pp. | MR

[3] B. V. Loginov, Yu. B. Rusak, “Obobschennaya zhordanova struktura v teorii vetvleniya”, Pryamye i obratnye zadachi dlya differentsialnykh uravnenii v chastnykh proizvodnykh i ikh prilozheniya, FAN, Tashkent, 1978, 133–148 | MR

[4] N. A. Sidorov, M. V. Falaleev, “Obobschennye resheniya differentsialnykh uravnenii s fredgolmovym operatorom pri proizvodnoi”, Differents. uravneniya, 23:4 (1987), 726–728 | MR | Zbl

[5] M. V. Falaleev, “O prilozheniyakh teorii fundamentalnykh operator-funktsii vyrozhdennykh integro-differentsialnykh operatorov v banakhovykh prostranstvakh”, Neklassicheskie uravneniya matematicheskoi fiziki, Izd-vo IM im. S. L. Soboleva SO RAN, Novosibirsk, 283–297

[6] M. V. Falaleev, S. S. Orlov, “Nachalno-kraevye zadachi dlya integro-differentsialnykh uravnenii vyazkouprugosti”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:4 (2010), 597–600 | MR

[7] M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. Ferreira, “Existence and Uniform Decay for a Non-Linear Viscoelastic Equation with Strong Damping”, Math. Meth. Appl. Sci., 24 (2001), 1043–1053 | DOI | MR | Zbl

[8] N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov–Schmidt Methods in Nonlinear Analysis and Applications, Kluwer Acad. Publ., Dordrecht–Boston–London, 2002, 548 pp. | MR | Zbl

[9] J. E. Munoz Rivera, L. H. Fatori, “Regularizing Properties and Propagations of Singularities for Thermoelastic Plates”, Math. Meth. Appl. Sci., 21 (1998), 797–821 | 3.0.CO;2-D class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[10] R. Racke, “Asymptotic Behavior of Solutions in Linear 2- or 3-d Thermoelasticity with Second Sound”, Quart Appl. Math., 61 (2003), 409–441 | MR