RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zh. Vychisl. Mat. Mat. Fiz.: Year: Volume: Issue: Page: Find

 Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 5, Pages 805–812 (Mi zvmmf467)

The Cauchy problem for a singularly perturbed Volterra integro-differential equation

N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: The Cauchy problem for a singularly perturbed Volterra integro-differential equation is examined. Two cases are considered: (1) the reduced equation has an isolated solution, and (2) the reduced equation has intersecting solutions (the so-called case of exchange of stabilities). An asymptotic expansion of the solution to the Cauchy problem is constructed by the method of boundary functions. The results are justified by using the asymptotic method of differential inequalities, which is extended to a new class of problems.

Key words: singularly perturbed Volterra integro-differential equation, Cauchy problem, asymptotic method, differential inequalities.

Full text: PDF file (954 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2006, 46:5, 768–775

Bibliographic databases:

UDC: 519.624.2

Citation: N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina, “The Cauchy problem for a singularly perturbed Volterra integro-differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 805–812; Comput. Math. Math. Phys., 46:5 (2006), 768–775

Citation in format AMSBIB
\Bibitem{NefNikUra06} \by N.~N.~Nefedov, A.~G.~Nikitin, T.~A.~Urazgil'dina \paper The Cauchy problem for a~singularly perturbed Volterra integro-differential equation \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2006 \vol 46 \issue 5 \pages 805--812 \mathnet{http://mi.mathnet.ru/zvmmf467} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2286277} \transl \jour Comput. Math. Math. Phys. \yr 2006 \vol 46 \issue 5 \pages 768--775 \crossref{https://doi.org/10.1134/S0965542506050046} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746056017} 

• http://mi.mathnet.ru/eng/zvmmf467
• http://mi.mathnet.ru/eng/zvmmf/v46/i5/p805

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. N. Nefedov, A. G. Nikitin, “The Cauchy problem for a singularly perturbed integro-differential Fredholm equation”, Comput. Math. Math. Phys., 47:4 (2007), 629–637
2. N. N. Nefedov, A. G. Nikitin, “The initial boundary value problem for a nonlocal singularly perturbed reaction–diffusion equation”, Comput. Math. Math. Phys., 52:6 (2012), 926–931
3. A. A. Archibasov, A. Korobeinikov, V. A. Sobolev, “Asymptotic expansions of solutions in a singularly perturbed model of virus evolution”, Comput. Math. Math. Phys., 55:2 (2015), 240–250
4. O. P. Filatov, “Globalnaya teorema suschestvovaniya i edinstvennosti resheniya pervoi kraevoi zadachi dlya nelineinogo integrodifferentsialnogo uravneniya parabolicheskogo tipa”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 3(125), 64–72
5. A. A. Bobodzhanov, V. F. Safonov, “A generalization of the regularization method to the singularly perturbed integro-differential equations with partial derivatives”, Russian Math. (Iz. VUZ), 62:3 (2018), 6–17
•  Number of views: This page: 200 Full text: 101 References: 32 First page: 1