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Bulletin of the MRSU / Section "Physics and mathematics" / 2013 № 4.

 

A.A. Akimov

[ON THE SOLUTION UNICITY OF NEUMANN TYPE FOR CHAPLYGIN EQUATION ] In: Bulletin of the Moscow Regional State University (electronic journal) [Bulletin of the Moscow Regional State University (electronic journal)], 2013, no. 4.


UDC Index: 517.95

Date of publication: 27.11.2013

The full text of the article

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Abstract


The article deals with the boundary-value problem for mixed type equations with Neumann boundary conditions in a mixed area for the Chaplygin equation. This problem arises in the study of a gas flow around an airfoil. While using the method of auxiliary functions the authors obtain a new uniqueness theorem to solve this problem with the modified Frankl condition for this type of problems without any restrictions other than smoothness on the elliptical part of the border area.

Key words


method of auxiliary functions, the Chaplygin equation, the Neumann condition, mixed type equations.

List of references


1. Sabitov K. B., Akimov A. A. K teorii analoga zadachi Neimana dlya uravneniya smeshannogo tipa Izvestiya vuzov. Matematika. ? 2001. No. 10. ? pp. 73?80.
2. Smirnov M.M. Uravneniya smeshannogo tipa. ? M.: Nauka, 1970. – 304 s.
3. Morawetz C.S. A uniqueness theorem for Francl's problem Commun. Pure and Appl. Math. ? 1954. ? No. 7. ? P. 697?700.
4. Protter M.H. Uniqueness theorems for the Tricomi problem J. Rational Mech. and Analysis. Part I, 2, 1. ? 1953. ? P. 107–114.

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