TY - JOUR

T1 - An Initial Boundary-value Problem for Hyperbolic Differential-operator Equations on a Finite Interval

AU - Yakubov, S

AU - Yakubov, Y

PY - 2004

Y1 - 2004

N2 - In this paper we give, for the first time, an abstract interpretation of initial boundary-value problems for hyperbolic equations such that a part of the boundary-value conditions contains also a differentiation of the time t of the same order as the equations. Initial boundary-value problems for hyperbolic equations 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 of the Cauchy problem, and for some special cases we give an expansion of a solution to the series of eigenvectors. As application we show, in particular, a generalization of the classical Fourier method of separation of variables.

AB - In this paper we give, for the first time, an abstract interpretation of initial boundary-value problems for hyperbolic equations such that a part of the boundary-value conditions contains also a differentiation of the time t of the same order as the equations. Initial boundary-value problems for hyperbolic equations 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 of the Cauchy problem, and for some special cases we give an expansion of a solution to the series of eigenvectors. As application we show, in particular, a generalization of the classical Fourier method of separation of variables.

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=tau-cris-version-2&SrcAuth=WosAPI&KeyUT=WOS:000208532500004&DestLinkType=FullRecord&DestApp=WOS_CPL

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SN - 0893-4983

VL - 17

SP - 53

EP - 72

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 1-2

ER -