Geodesic
A Boundary Function Method for Solving the Model Lighthill Equation with a Regular Singular Point
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 819-824 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove that it is possible to apply a method similar to the Vishik–Lyusternik–Vasileva–Imanaliev boundary function method for constructing the asymptotics of the solution of the model Lighthill equation with a regular singular point.
Keywords: model Lighthill equation, boundary function method, Cauchy problem, contraction operator, Lagrange inequality
Mots-clés : Fréchet derivative. 
@article{MZM_2012_92_6_a1,
     author = {K. Alymkulov and A. A. Khalmatov},
     title = {A {Boundary} {Function} {Method} for {Solving} the {Model} {Lighthill} {Equation} with a {Regular} {Singular} {Point}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {819--824},
     year = {2012},
     volume = {92},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a1/}
}
TY  - JOUR
AU  - K. Alymkulov
AU  - A. A. Khalmatov
TI  - A Boundary Function Method for Solving the Model Lighthill Equation with a Regular Singular Point
JO  - Matematičeskie zametki
PY  - 2012
SP  - 819
EP  - 824
VL  - 92
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a1/
LA  - ru
ID  - MZM_2012_92_6_a1
ER  - 
%0 Journal Article
%A K. Alymkulov
%A A. A. Khalmatov
%T A Boundary Function Method for Solving the Model Lighthill Equation with a Regular Singular Point
%J Matematičeskie zametki
%D 2012
%P 819-824
%V 92
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a1/
%G ru
%F MZM_2012_92_6_a1
K. Alymkulov; A. A. Khalmatov. A Boundary Function Method for Solving the Model Lighthill Equation with a Regular Singular Point. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 819-824. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a1/

[1] M. G. Lighthill, “A technique for rendering approximate solution to physical problems uniformly valid”, Philos. Mag. (7), 40 (1949), 1179–1201 | MR | Zbl

[2] K. Alymkulov, Vozmuschennye differentsialnye uravneniya s osobymi tochkami i nekotorye problemy bifurkatsionnykh zadach, Ilim, Bishkek, 1992 | Zbl

[3] K. Alymkulov, Zh. K. Zheentaeva, “Metod strukturnogo sraschivaniya resheniya modelnogo uravneniya Laitkhilla s regulyarnoi osoboi tochkoi”, Matem. zametki, 79:5 (2006), 643–652 | MR | Zbl

[4] M. Imanaliev, Asimptoticheskie metody v teorii singulyarno-vozmuschennykh integro-differentsialnykh sistem, Ilim, Bishkek, 1972 | MR

[5] V. A. Trenogin, “Razvitie i prilozhenie asimptoticheskogo metoda Lyusternika–Vishika”, UMN, 25:4 (1970), 123–156 | MR | Zbl

[6] A. B. Vasileva, V. F. Butuzov, Asimptoticheskie razlozheniya reshenii singulyarno-vozmuschennykh uravnenii, Nauka, M., 1973 | MR | Zbl

[7] K. Alymkulov, Materialy mezhdunarodnoi konferentsii “Differentsialnye uravneniya i smezhnye voprosy”, posvyaschennoi pamyati I. G. Petrovskogo (21–26 maya 2007 g.), MGU, M., 2007

[8] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl