Invariance of integro-differential equations with moving region of integration

• Autorzy: Zawistowski Z. J.
• Języki publikacji: EN

Abstrakty

EN

General criterion of invariance of integro-differential equations under the Lie symmetry group of point transformations is derived. It is a generalization of the previous form of the criterion to the case of a moving range of integration. This is the situation when a region of integration depends on external, with respect to integration, variables what leads to its explicit dependence on a group parameter, so the region of integration moves under symmetry transformations. General case of dependence on independent and dependent variables and their derivatives is considered.

Słowa kluczowe

EN

symmetry; integro-differential equations; Lie groups

PL

symetria; równanie całkowo-różniczkowe; grupa Liego

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2006
• Tom: Vol. 47, no 2
• Strony: 103--112
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Zawistowski Z. J.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świetokrzyska 21, 00-049 Warszawa, Poland,

Bibliografia

• 1. L. V. OVSIANNIKOV, Group analysis of differential equations. Academic Press, Boston 1982.
• 2. N. Ch. IBRAGIMOV, Transformation groups applied to mathematical physics, Reidel, Dordrecht 1985.
• 3. P. J. OLVER, Applications of lie groups to differential equations. Springer, New York 1986.
• 4. G. W. BLUMAN, S. KUMEI, Symmetries and differential equations, Springer, New York 1989.
• 5. H. STEPHANI, Differential equations. Their solutions using symmetries, M. Mc CALLUM (Ed.), Cambridge University Press, Cambridge 1989.
• 6. Z. J. ZAWISTOWSKI, Rep. Math. Phys. 48, 1/2, 269, 2001.
• 7. Z. J. ZAWISTOWSKI, Proceedings of the Institute of Mathematics of NAS of Ukraine 43, Part 1, 263, 2002.
• 8. Z. J. ZAWISTOWSKI, Rep. Math. Phys. 54, 2, 341, 2004.
• 9. I.M. GELFAND, S.W. FOMIN, Calculus of variations, Englewood Cliff, Prentice-Hall, 1962.
• 10. Z. J. ZAWISTOWSKI, Rep. Math. Phys. 50, 2, 125, 2002.
• 11. R. T. GLASSEY, The Cauchy Problem in Kinetic Theory, SIAM, Philadelphia 1992.
• 12. V.I. FUSHCHICH, V.M. SHTELEN, N.I SEROV: Symmetry analysis and exact solutions of equations of nonlinear mathematical physics, Kluwer Academic Publishers, Dordrecht 1993.
• 13. N.H. IBRAGIMOV (Editor), CRC handbook of Lie group analysis of differential equations, Boca Raton, Florida, CRC Press, Inc., Vol.1, 1994; Vol.2, 1995; Vol.3, 1996.
• 14. N.H. IBRAGIMOV, V.N. KOVALEV, V.V. PUSTOVALOV, Nonlinear Dynamics, 28, 135, 1971.
• 15. V.B. TARANOV, ZhTF 46, 1271, [in Russian], English translation: Sov. Tech. Phys., 21, 720, 1976.
• 16. B.K. HARRISON, F.B. ESTABROOK, J. Math. Phys., 12, 4, 653, 1971.
• 17. Yu.N. GRIGORIEV, S.V. MELESHKO, Dokl. Akad. Nauk SSSR [in Russian], 297, 2, 323, 1987.
• 18. Yu.N. GRIGORIEV, S.V. MELESHKO, Arch. Mech., 42, 6, 693, 1990.
• 19. V.N. KOVALEV, S.V. KRIVENKO, V.V. PUSTOVALOV, Pisma Zh. Exper. Teoret. Fiz [in Russian], 55, 4, 256; English transl. [in:] JEPT Lett., 1992.
• 20. V.N. KOVALEV, S.V. KRIVENKO, V.V. PUSTOVALOV, J. Nonlinear Math. Phys., 3, 1-2, 175, 1996.
• 21. A.M. VINOGRADOV, I.S. KRASILSHCHIK, Acta Applicandae Mathematicae, 2, 1, 79, 1984.
• 22. A.M. VINOGRADOV, I.S KRASILSHCHIK [Eds.], Symmetries and conservation laws for equations of mathematical physics, Moscow, Factorial, 1997 (in Russian); The English translation of the book: Translations of Mathematical Monographs, Vol. 182, American Mathematical Society, Providence, Rhode Island, 1999.
• 23. V.N. CHETVERIKOV, A.G. KUDRYAVTSEV, Acta Applicandae Mathematicae, 1-3, 45-56, 1995.