A system of differential-operator Equations of different orders in Hilbert spaces

Angelo Favini; Yakov Yakubov

doi:10.1007/s00009-007-0110-5

A system of differential-operator Equations of different orders in Hilbert spaces

Angelo Favini^*, Yakov Yakubov

^*Corresponding author for this work

School of Mathematical Sciences

University of Bologna

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an abstract Cauchy problem for a system of nonhomogeneous abstract differential equations in Hilbert spaces. The "main" equation is of the second order and "boundary" equations are of the first order. Existence of a solution is proved. Application to mixed (initial boundary-value) problems for one-dimensional second order hyperbolic equations and for fourth order PDEs with the time derivative in boundary conditions has been shown.

Original language	English
Pages (from-to)	163-177
Number of pages	15
Journal	Mediterranean Journal of Mathematics
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/s00009-007-0110-5
State	Published - Jul 2007

Keywords

Abstract Cauchy problem
Degenerate abstract equations
Existence
Hyperbolic equations

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10.1007/s00009-007-0110-5

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keywords = "Abstract Cauchy problem, Degenerate abstract equations, Existence, Hyperbolic equations",

author = "Angelo Favini and Yakov Yakubov",

note = "Funding Information: The first author was partially supported by 60% funds of the University of Bologna and G.N.A.M.P.A. of INdAM; the second author was supported by the Israel Ministry of Absorption.",

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N2 - We consider an abstract Cauchy problem for a system of nonhomogeneous abstract differential equations in Hilbert spaces. The "main" equation is of the second order and "boundary" equations are of the first order. Existence of a solution is proved. Application to mixed (initial boundary-value) problems for one-dimensional second order hyperbolic equations and for fourth order PDEs with the time derivative in boundary conditions has been shown.

AB - We consider an abstract Cauchy problem for a system of nonhomogeneous abstract differential equations in Hilbert spaces. The "main" equation is of the second order and "boundary" equations are of the first order. Existence of a solution is proved. Application to mixed (initial boundary-value) problems for one-dimensional second order hyperbolic equations and for fourth order PDEs with the time derivative in boundary conditions has been shown.

KW - Abstract Cauchy problem

KW - Degenerate abstract equations

KW - Existence

KW - Hyperbolic equations

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A system of differential-operator Equations of different orders in Hilbert spaces

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