Global existence for a wave equation on ℝN

Papadopoulos, PG; Stavrakakis, NM

dc.contributor.author	Papadopoulos, PG	en
dc.contributor.author	Stavrakakis, NM	en
dc.date.accessioned	2014-03-01T01:57:09Z
dc.date.available	2014-03-01T01:57:09Z
dc.date.issued	2008	en
dc.identifier.issn	19371632	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28362
dc.subject	Blow-up	en
dc.subject	Concavity method	en
dc.subject	Dissipation	en
dc.subject	Generalised sobolev spaces	en
dc.subject	Global solution	en
dc.subject	Kirchhoff strings	en
dc.subject	Potential well	en
dc.subject	Quasilinear hyperbolic equations	en
dc.subject	Unbounded domains	en
dc.subject	Weighted Lp spaces	en
dc.title	Global existence for a wave equation on ℝN	en
heal.type	journalArticle	en
heal.identifier.primary	10.3934/dcdss.2008.1.139	en
heal.identifier.secondary	http://dx.doi.org/10.3934/dcdss.2008.1.139	en
heal.publicationDate	2008	en
heal.abstract	We study the initial value problem for some degenerate non-linear dissipative wave equations of Kirchhoff type: (Equation Presented) with initial conditions u(x, 0) = u0(x) and ut(x, 0) = u1(x), in the case where N ≥ 3, δ > 0, γ ≥ 1, f(u) = \|u\|au with a > 0 and (φ(x))-1 = g(x) is a positive function lying in LN/2(ℝN) ∩ L∞(ℝN). If the initial data {u0,u1} are small and ∥ ∇ u0∥ > 0, then the unique solution exists globally and has certain decay properties.	en
heal.journalName	Discrete and Continuous Dynamical Systems - Series S	en
dc.identifier.doi	10.3934/dcdss.2008.1.139	en
dc.identifier.volume	1	en
dc.identifier.issue	1	en
dc.identifier.spage	139	en
dc.identifier.epage	149	en