Nonlinear wave equations on a class of bounded fractal sets

The nonlinear wave equation u tt=Δu+f(u) with given initial data and zero boundary conditions on a class of bounded self-similar fractal sets is investigated. The Sobolev-type inequality is the starting point of this work, which holds for a class of fractals including the well-known Sierpı&#x030...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2002-06, Vol.270 (2), p.657-680
Main Author: Hu, Jiaxin
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
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Summary:The nonlinear wave equation u tt=Δu+f(u) with given initial data and zero boundary conditions on a class of bounded self-similar fractal sets is investigated. The Sobolev-type inequality is the starting point of this work, which holds for a class of fractals including the well-known Sierpı́nski gasket. We obtain the global existence of strong solutions for suitable f if the spectral dimension d s of the fractal satisfies d s
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00102-6