The method of integro-differential equations and continued fractions in the problem of parametric excitation of waves

S. M. Zen'kovskaya   ; V. I. Yudovich

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 4, pp. 731-745

Bibliographie

[1] Hadamard J., “Sur les ondes liquides”, C. r. Acad. sci., 150 (1910), 609–611 ; 772–774 ; Atti Accad. Lincei, 25:5 (1916), 716–719 | Zbl

[2] Sretenskii L. N., Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977

[3] Cherepanov A. A., Vliyanie peremennykh vneshnikh polei na neustoichivost Releya-Teilora, Preprint; Некоторые задачи устойчивости поверхностей жидкости, УНЦ АН СССР, Свердловск, 1984, 29–53

[4] Shmidt G., Parametricheskie kolebaniya, Mir, M., 1978 | MR

[5] Yakubovich V. A., Starzhinskii V. M., “Parametricheskii rezonans sistem so mnogimi stepenyami svobody”, Tr. mezhvuz. konf. po prikl. teorii ustoichivosti dvizheniya i analitich. mekhan., Kazan, 1964, 123–134

[6] Strett M. D. O., Funktsii Lyame, Mate i rodstvennye im v fizike i tekhnike, Nauchno-tekhn. izd-vo Ukrainy, Kharkov, 1935

[7] Valeev K. G., “Ob ustoichivosti reshenii lineinykh differentsialnykh uravnenii vtorogo poryadka s sinusoidalnymi koeffitsientami”, Izv. vuzov. Radiofiz., 1962, no. 5, 766–783

[8] Markman G. S., Yudovich V. I., “Chislennoe issledovanie vozniknoveniya konvektsii v sloe zhidkosti pod deistviem periodicheskikh po vremeni vneshnikh sil”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1972, no. 3, 81–86

[9] Markman G. S., Yudovich V. I., “Vozniknovenie konvektsionnykh rezhimov dvoinogo perioda v periodicheskom pole vneshnikh sil”, Prikl. mekhan. i tekhn. fiz., 1972, no. 6, 65–70

[10] Belenkaya L. Kh., Yudovich V. I., “Ustoichivost vyazkouprugogo sterzhnya pod deistviem periodicheskoi nagruzki”, Izv. AN SSSR. Mekhan. tverdogo tela, 1978, no. 6, 146–152

[11] Belenkaya L. Kh., Yudovich V. I., Ustoichivost vyazkouprugogo sterzhnya pod deistviem periodicheskoi sily, Dep. v VINITI, No 2367-78

[12] Yudovich V. I., “Metod tsepnykh drobei v spektralnoi teorii lineinykh differentsialnykh operatorov s periodicheskimi koeffitsientami”, Yubileinyi sb., posvyaschennyi 75-letiyu V. A. Kakicheva, Gos. un-t, Novgorod, 2001, 20–24

[13] Meshalkin L. D., Sinai A. G., “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Prikl. matem. i mekhan., 25:6 (1961), 1140–1143 | Zbl

[14] Yudovich V. I., “Primer rozhdeniya vtorichnogo statsionarnogo ili periodicheskogo techeniya pri potere ustoichivosti laminarnogo techeniya vyazkoi neszhimaemoi zhidkosti”, Prikl. matem. i mekhan., 29:3 (1965), 453–467 | Zbl

[15] Zenkovskaya S. M., “Ob ustoichivosti odnogo periodicheskogo resheniya uravneniya Nave–Stoksa”, Prikl. matem. i mekhan., 31:1 (1967), 124–130

[16] Belenkaya L., Friedlander S., Yudovich V. I., “The unstable spectrum of oscilating shear flows”, SIAM J. Appl. Math., 59:5 (1999), 1701–1715 | DOI | MR | Zbl

[17] Yudovich V. I., “Dlinnovolnovaya asimptotika v kinematicheskoi probleme magnitnogo dinamo”, Izv. vuzov. Severo-kavkazskii region. Estestvennye nauki, 2001, Spetsvypusk, 155–160

[18] Khovanskii A. N., Prilozhenie tsepnykh drobei i ikh obobschenii k voprosam priblizhennogo analiza, Gostekhteorizdat, M., 1956

[19] Yudovich V. I., Metod linearizatsii v gidrodinamicheskoi teorii ustoichivosti, Rostovskii un-t, Rostov-na-Donu, 1984 | Zbl

[20] Krein S. G., Kopachevskii N. D., Ngo Zui Kan, Operatornye metody v lineinoi gidrodinamike. Evolyutsionnye i spektralnye zadachi, Nauka. Fizmatlit, M., 1989 | MR

[21] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR | Zbl

[22] Yudovich V. I., Lektsii ob uravneniyakh matematicheskoi fiziki, “Ekspertnoe byuro”, Rostov-na-Donu, 1998

[23] Polia G., Sege G., Zadachi i teoremy iz analiza, v. II, Gostekhteorizdat, M., 1956

[24] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971

[25] Lamb G., Gidrodinamika, Gostekhizdat, M., 1947