Electron. J. Diff. Equ., Vol. 2016 (2016), No. 230, pp. 1-16.

Integrability of the limit model for a vacuum diode and a solution to the singular boundary-value problem

Alexander A. Kosov, Edward I. Semenov, Alexander V. Sinitsyn

Abstract:
This article concerns singular boundary-value problems for a vacuum diode model. We prove the integrability of a system of nonlinear differential equations and construct a complete system of the first integrals; thus developing a method for solving singular boundary value problems. Also we study the asymptotic behavior of the solution in a neighborhood of the singular point.

Submitted August 4, 2015. Published August 23, 2016.
Math Subject Classifications: 34B16, 34B60, 35Q83.
Key Words: First integrals; singular boundary value problem; vacuum diode.

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Alexander A. Kosov
Matrosov Institute for System Dynamics and Control Theory
Siberian Branch of Russian Academy of Sciences
ISDCT SB RAS Lermontov str., 134, Post Box 292
664033, Irkutsk, Russia
email: aakosov@yandex.ru
Edward I. Semenov
Matrosov Institute for System Dynamics and Control Theory
Siberian Branch of Russian Academy of Sciences
ISDCT SB RAS Lermontov str., 134, Post Box 292
664033, Irkutsk, Russia
email: edwseiz@gmail.com
Alexander V. Sinitsyn
Universidad Nacional de Colombia
Departamento de Matematicas
Bogota, Colombia
email: avsinitsyn@yahoo.com

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