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  Global pointwise decay estimates for defocusing radial nonlinear wave equations

Bieli, R., & Szpak, N. (2011). Global pointwise decay estimates for defocusing radial nonlinear wave equations. Communications in Partial Differential Equations, 36(2), 205-215. doi:10.1080/03605302.2010.531072.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-605D-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-605F-E
Genre: Journal Article

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 Creators:
Bieli, Roger1, Author              
Szpak, Nikodem1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping adjusted to the nonlinearity. As a result we obtain a pointwise bound on the solutions for arbitrarily large Cauchy data, provided the solutions exist globally. The decay rates are identical with those for small data and hence seem to be optimal. A generalization beyond the spherical symmetry is suggested.

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 Dates: 2011
 Publication Status: Published in print
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 Identifiers: eDoc: 429175
arXiv: 0903.0799
DOI: 10.1080/03605302.2010.531072
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Title: Communications in Partial Differential Equations
Source Genre: Journal
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Publ. Info: New York : Marcel Dekker
Pages: - Volume / Issue: 36 (2) Sequence Number: - Start / End Page: 205 - 215 Identifier: ISSN: 0360-5302
CoNE: /journals/resource/954925521677