Geodesic
Unique solvability of pseudohyperbolic equations with singular right-hand sides
Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 582-595 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider the solvability of the Cauchy problem for pseudohyperbolic equations (partial differential equations of third order). For the case in which the right-hand side is a generalized function (distribution) of finite order, we establish a theorem on the unique solvability for a sufficiently general pseudohyperbolic operator. The method of proof is based on a specially constructed “scale” of a priori inequalities for the direct and adjoint operators. 
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D. A. Nomirovskii. Unique solvability of pseudohyperbolic equations with singular right-hand sides. Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 582-595. http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a11/

[1] S. S. Voit, “Rasprostranenie nachalnykh uplotnenii v vyazkom gaze”, Uchenye zapiski MGU. Mekh. 5, 172, 1954, 125–142 | Zbl

[2] I. I. Suveika, “Smeshannye zadachi dlya uravneniya rasprostraneniya vozmuschenii v vyazkikh sredakh”, Differents. uravneniya, 19:2 (1983), 337–347 | MR

[3] A. N. Guz, Dinamika szhimaemoi vyazkoi zhidkosti, A.S.K., Kiev, 1998

[4] V. M. Bulavatskii, I. I. Yurik, “Matematicheskoe modelirovanie protsessa teploperenosa v relaksiruyuschei srede”, Dopovidi NAN Ukraïni, 1996, no. 7, 42–45 | MR

[5] S. M. Ponomarev, “K voprosu o povedenii vyazkoi szhimaemoi zhidkosti pod deistviem zadannogo granichnogo rezhima”, Differents. uravneniya, 22:4 (1986), 719–722 | MR | Zbl

[6] A. I. Kozhanov, “Zadacha s kosoi proizvodnoi dlya nekotorykh psevdoparabolicheskikh i blizkikh k nim uravnenii”, Sib. matem. zh., 37:6 (1996), 1335–1346 | MR | Zbl

[7] V. A. Malovichko, “O kraevykh zadachakh dlya vyrozhdayuschikhsya psevdoparabolicheskikh i psevdogiperbolicheskikh sistem”, Differents. uravneniya, 27:12 (1991), 2120–2124 | MR | Zbl

[8] L. I. Palienko, Modelyuvannya ta uzagalnena optimizatsiya u psevdogiperbolichnikh sistemakh, Diss. ... k.f.-m.n., KNU, Kiev, 1999

[9] I. I. Lyashko, S. I. Lyashko, D. A. Klyushin, A. Yu. Spivak, “Chislennoe reshenie psevdogiperbolicheskikh uravnenii”, Dopovidi NAN Ukraïni, 1998, no. 5, 29–34 | MR | Zbl

[10] S. I. Lyashko, Obobschennoe upravlenie lineinymi sistemami, Naukova dumka, Kiev, 1998 | Zbl

[11] D. A. Nomirovskii, “Upravlenie v psevdogiperbolicheskikh sistemakh”, Vychisl. i prikl. matem., 1996, no. 80, 68–77 | Zbl

[12] I. I. Lyashko, S. I. Lyashko, D. A. Nomirovskii, “Upravlyaemost giperbolicheskikh i psevdogiperbolicheskikh sistem v klasse singulyarnykh vozdeistvii”, Dopovidi NAN Ukraïni, 2000, no. 11, 131–134 | MR | Zbl

[13] S. I. Lyashko, V. V. Semenov, “Ob upravlyaemosti lineinykh raspredelennykh sistem v klassakh obobschennykh vozdeistvii”, Kibernetika i sistemnyi analiz, 2001, no. 1, 18–41 | MR | Zbl

[14] S. I. Lyashko, Generalized Optimal Control of Linear Systems with Distributed Parameters, Kluwer, Boston, 2002 | MR | Zbl

[15] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR | Zbl

[16] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 | MR

[17] Funktsionalnyi analiz, SMB, ed. S. G. Krein, Nauka, M., 1972 | MR | Zbl

[18] I. I. Lyashko, V. P. Didenko, O. E. Tsitritskii, Filtratsiya shumov, Naukova dumka, Kiev, 1979 | MR | Zbl

[19] S. G. Krein, Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971 | MR | Zbl

[20] C. I. Lyashko, D. A. Nomirovskii, “Obobschennoe reshenie i optimalnoe upravlenie v sistemakh, opisyvayuschikh dinamiku vyazkoi stratifitsirovannoi zhidkosti”, Differents. uravneniya, 39:1 (2003), 84–91 | MR