The Floquet Theory of the Periodic Euler-Bernoulli Equation

Papanicolaou, VG; Kravvaritis, D

dc.contributor.author	Papanicolaou, VG	en
dc.contributor.author	Kravvaritis, D	en
dc.date.accessioned	2014-03-01T01:14:14Z
dc.date.available	2014-03-01T01:14:14Z
dc.date.issued	1998	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12942
dc.subject	Algebraic/geometric multiplicity	en
dc.subject	Euler-Bernoulli equation for the vibrating beam	en
dc.subject	Floquet spectrum	en
dc.subject	Pseudospectrum	en
dc.subject.classification	Mathematics	en
dc.subject.other	SCHRODINGER-OPERATORS	en
dc.subject.other	SPECTRAL THEORY	en
dc.subject.other	VIBRATING BEAM	en
dc.title	The Floquet Theory of the Periodic Euler-Bernoulli Equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jdeq.1998.3474	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jdeq.1998.3474	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	We continue the study (initiated in [17]) of the spectral theory of the fourth-order eigenvalue problem [a(x) u "(x)]" = lambda rho(x) u(x), - infinity <x <infinity, where the functions a and p are periodic and strictly positive. This equation models the transverse vibrations of a thin straight (periodic) beam whose physical characteristics are described by a and p. The equality of the algebraic and geometric multiplicities of the periodic and antiperiodic eigenvalues is established. Also a spectrum-like set, that we called "pseudospectrum" or "psi-spectrum," is introduced (or, rather, discovered). This psi-spectrum is shown to lie on the negative real axis and have a band-gap structure. Various open questions and conjectures are mentioned at the end of the paper. (C) 1998 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1006/jdeq.1998.3474	en
dc.identifier.isi	ISI:000077460400002	en
dc.identifier.volume	150	en
dc.identifier.issue	1	en
dc.identifier.spage	24	en
dc.identifier.epage	41	en