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dc.contributor.authorGeorgiev, Svetlin G. ( )
dc.date.accessioned2021-04-26T14:45:23Z
dc.date.available2021-04-26T14:45:23Z
dc.date.issued2004-05-26
dc.identifier.citationGeorgiev, S. G. (2004). Blow-up of solutions to a nonlinear wave equation. Electronic Journal of Differential Equations, 2004(77), pp. 1-7.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13431
dc.description.abstract

We study the solutions to the radial 2-dimensional wave equation

Xtt - 1/ r Xr - Xrr + sinh2X/ 2r2 = g,
X(1, r) = X∘ ∈ Ḣγrad, Xt(1, r) = X1 ∈ Ḣγ-1rad,

where r = |x| and x in ℝ2. We show that this Cauchy problem, with values into a hyperbolic space, is ill posed in subcritical Sobolev spaces. In particular, we construct a function g(t, r) in the space Lp ([0, 1]Lqrad), with 1/p + 2/q = 3 - γ, 0 < γ < 1, p ≥ 1, and 1 < q ≤ 2, for which the solution satisfies limt→0 ∥x̄∥γrad = ∞. In doing so, we provide a counterexample to estimates in [1].

dc.formatText
dc.format.extent7 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectWave equationen_US
dc.subjectBlow-upen_US
dc.subjectHyperbolic spaceen_US
dc.titleBlow-up of solutions to a nonlinear wave equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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