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

Angelo Favini*, Yakov Yakubov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)163-177
Number of pages15
JournalMediterranean Journal of Mathematics
Volume4
Issue number2
DOIs
StatePublished - Jul 2007

Funding

FundersFunder number
Israel Ministry of Absorption
Istituto Nazionale di Alta Matematica "Francesco Severi"
Università di Bologna

    Keywords

    • Abstract Cauchy problem
    • Degenerate abstract equations
    • Existence
    • Hyperbolic equations

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