Nonlinear dissipative eigenvalue problems with large initial conditions

Papanicolaou, VG; Newton, PK

dc.contributor.author	Papanicolaou, VG	en
dc.contributor.author	Newton, PK	en
dc.date.accessioned	2014-03-01T01:22:49Z
dc.date.available	2014-03-01T01:22:49Z
dc.date.issued	2005	en
dc.identifier.issn	0022-2488	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16669
dc.subject.classification	Physics, Mathematical	en
dc.title	Nonlinear dissipative eigenvalue problems with large initial conditions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1063/1.1829154	en
heal.identifier.secondary	013502	en
heal.identifier.secondary	http://dx.doi.org/10.1063/1.1829154	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We consider the initial value problem mu'' + phi(t)mu' + B(2)mu(2p+1) =0, t greater then 0, mu(0)=gamma, mu'(0)=0, where rho is a positive integer, B, gamma are positive parameters, and phi(t) is a positive function. The differential equation describes a (dissipative) oscillatory system whose amplitude A(t) decreases in time. For a given time b greater than 0, our task is to compute the asymptotics of A(b), as gamma-->infinity. In the case where phiis an element of C-1(0, infinity)boolean and L-1(0, epsilion), we give an explicit answer. We also discuss the case where phi(t)=2/t. This case is of particular interest since it is related to the nonlinear Schrodinger equation in three dimensions. (C) 2005 American Institute of Physics.	en
heal.publisher	AMER INST PHYSICS	en
heal.journalName	Journal of Mathematical Physics	en
dc.identifier.doi	10.1063/1.1829154	en
dc.identifier.isi	ISI:000226921200030	en
dc.identifier.volume	46	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	10	en