On the limit behaviour of the spectrum of a model problem for the Orr-Sommerfeld equation with Poiseuille profile

Izvestiya Mathematics

Volumn 66, Issue 4, 2002, Pages 829-856

  Shkalikov, A A ^a   Tumanov, S N ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747160336     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2002v066n04ABEH000399     Document Type: Article

References (9)

1. A. A. Shkalikov, "The limit behaviour of the spectrum for large parameter values in a model problem", Mat. Zametki 62 (1997), 950-953;
2. English transl., Math. Notes 62 (1997), 796-799.
3. S. G. Roddy, P. J. Schmidt and D. S. Henningson, "Pseudospectra of the Orr-Sommerfeld operator", SIAM J. Appl. Math. 53:1 (1993), 15-47.
4. V. A. Marchenko, Sturm-Liouville operators and applications, Naukova Dumka, Kiev 1977; English transl., Birkhauser, Basel 1986.
5. M. A. Naimark, Linear differential operators, Nauka, Moscow 1969; English transl. of an earlier edition, Ungar, New York 1967, 1968.
6. M. V. Fedoryuk, Asymptotic methods for linear ordinary differential equations, Nauka, Moscow 1983;
7. English transl., Asymptotic analysis: linear ordinary differential equations, Springer, Berlin 1993.
8. F. W. J. Olver, Asymptotics and special functions, Academic Press, New York-London 1974; Russian transl., Nauka, Moscow 1990.
9. S. N. Tumanov, "Model problem for Poiseuille profile. Critical spectrum curve", Internat. Conf. "Diff. equations and related topics" dedicated to the Centenary of I. G. Petrovskii, Book of Abstracts, Moscow State Univ. Press, Moscow 2001, pp. 413-414.