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dc.contributor.authorPapadopoulos, Perikles G. ( Orcid Icon 0000-0002-8268-253X )
dc.contributor.authorStavrakakis, Nikolaos M. ( )
dc.identifier.citationPapadopoulos, P. G., & Stavrakakis, N. M. (2006). Strong global attractor for a quasilinear nonlocal wave equation on ℝN. Electronic Journal of Differential Equations, 2006(77), pp. 1-10.en_US

We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation

utt - ϕ(x) ∥∇u(t)∥2 ∆u + δut + |u|α u = 0,

in ℝN, t ≥ 0, with initial conditions u(x, 0) = u0(x) and ut(x, 0) = u1(x). We consider the case N ≥ 3, δ > 0, and (ϕ(x))-1 a positive function in LN/2(ℝN) ∩ L∞(ℝN). The existence of a global attractor is proved in the strong topology of the space D1,2(ℝN) x L2g(ℝN).

dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectQuasilinear hyperbolic equationsen_US
dc.subjectKirchhoff stringsen_US
dc.subjectGlobal attractoren_US
dc.subjectUnbounded domainsen_US
dc.subjectGeneralized Sobolev spacesen_US
dc.subjectWeighted Lp spacesen_US
dc.titleStrong global attractor for a quasilinear nonlocal wave equation on ℝNen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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