HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL

Sasun Yakubov; Yakov Yakubov

HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL

Sasun Yakubov, Yakov Yakubov

School of Mathematical Sciences

University of Haifa

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we give, for the first time, an abstract interpretation of such initialboundary value problems for hyperbolic equations that a part of boundary valueconditions contains also a differentiation on the time of thesame order as equations.A similar situation for parabolic and elliptic equations has been studied in [YYa2,section 7.2.10] and [YakS], respectively. Initial boundary value problems for hyperbolicequations are reduced to the Cauchy problem for a system of hyperbolic differential-operator equations. A solution of this system is not a vector-function but one function.At the same time, the system is not overdetermined. We prove the well-posedness ofthe Cauchy problem and for some special cases we give an expansion of a solution tothe series of eigenvectors. As application we show, in particular, a generalization of theclassical Fourier method of separation of variables.

Original language	English
Title of host publication	Spectral and evolution problems
Subtitle of host publication	proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi
Editors	N. D. Kopachevsky, I. V. Orlov
Place of Publication	Simferopol, Crimea, Ukraine
Publisher	Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science
Pages	234-244
Number of pages	11
Volume	14
State	Published - 2004
Event	Crimean Autumn Mathematical School-Symposium, Proceedings - Sevastopol, Laspi, Ukraine Duration: 18 Sep 2003 → 29 Sep 2003 Conference number: 14

Publication series

Name	Spectral and evolution problems; Спектральные и эволюционные задачи
Publisher	Taurida National V. Vernadsky University; Black Sea Branch of Moscow State University; Crimean Scientific Center of Ukrainian NAS; Crimean Academy of Sciences; Crimean Mathematical Foundation, 2004.
Volume	14

Conference

Conference	Crimean Autumn Mathematical School-Symposium, Proceedings
Abbreviated title	KROMSH
Country/Territory	Ukraine
City	Sevastopol, Laspi
Period	18/09/03 → 29/09/03

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Yakubov, S., & Yakubov, Y. (2004). HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL. In N. D. Kopachevsky, & I. V. Orlov (Eds.), Spectral and evolution problems: proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi (Vol. 14, pp. 234-244). (Spectral and evolution problems; Спектральные и эволюционные задачи; Vol. 14). Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science. https://epdf.tips/spectral-and-evolution-problems-proceedings-14th-crimean-autumn-mathematical-sch.html

Yakubov, Sasun ; Yakubov, Yakov. / HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL. Spectral and evolution problems: proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi. editor / N. D. Kopachevsky ; I. V. Orlov. Vol. 14 Simferopol, Crimea, Ukraine : Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science, 2004. pp. 234-244 (Spectral and evolution problems; Спектральные и эволюционные задачи).

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title = "HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL",

abstract = "In this paper we give, for the first time, an abstract interpretation of such initialboundary value problems for hyperbolic equations that a part of boundary valueconditions contains also a differentiation on the time of thesame order as equations.A similar situation for parabolic and elliptic equations has been studied in [YYa2,section 7.2.10] and [YakS], respectively. Initial boundary value problems for hyperbolicequations are reduced to the Cauchy problem for a system of hyperbolic differential-operator equations. A solution of this system is not a vector-function but one function.At the same time, the system is not overdetermined. We prove the well-posedness ofthe Cauchy problem and for some special cases we give an expansion of a solution tothe series of eigenvectors. As application we show, in particular, a generalization of theclassical Fourier method of separation of variables.",

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Yakubov, S & Yakubov, Y 2004, HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL. in ND Kopachevsky & IV Orlov (eds), Spectral and evolution problems: proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi. vol. 14, Spectral and evolution problems; Спектральные и эволюционные задачи, vol. 14, Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science, Simferopol, Crimea, Ukraine, pp. 234-244, Crimean Autumn Mathematical School-Symposium, Proceedings, Sevastopol, Laspi, Ukraine, 18/09/03. <https://epdf.tips/spectral-and-evolution-problems-proceedings-14th-crimean-autumn-mathematical-sch.html>

HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL. / Yakubov, Sasun; Yakubov, Yakov.
Spectral and evolution problems: proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi. ed. / N. D. Kopachevsky; I. V. Orlov. Vol. 14 Simferopol, Crimea, Ukraine: Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science, 2004. p. 234-244 (Spectral and evolution problems; Спектральные и эволюционные задачи; Vol. 14).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper we give, for the first time, an abstract interpretation of such initialboundary value problems for hyperbolic equations that a part of boundary valueconditions contains also a differentiation on the time of thesame order as equations.A similar situation for parabolic and elliptic equations has been studied in [YYa2,section 7.2.10] and [YakS], respectively. Initial boundary value problems for hyperbolicequations are reduced to the Cauchy problem for a system of hyperbolic differential-operator equations. A solution of this system is not a vector-function but one function.At the same time, the system is not overdetermined. We prove the well-posedness ofthe Cauchy problem and for some special cases we give an expansion of a solution tothe series of eigenvectors. As application we show, in particular, a generalization of theclassical Fourier method of separation of variables.

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Yakubov S, Yakubov Y. HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL. In Kopachevsky ND, Orlov IV, editors, Spectral and evolution problems: proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003), September 18-29, 2003, Sevastopol, Laspi. Vol. 14. Simferopol, Crimea, Ukraine: Taurida National V. Vernadsky University, Crimean Mathematical Foundation, Crimean Academy of Science. 2004. p. 234-244. (Spectral and evolution problems; Спектральные и эволюционные задачи).

HYPERBOLIC DIFFERENTIAL-OPERATOR EQUATIONS ON A FINITE INTERVAL

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