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Small solutions to nonlinear wave equations in the Sobolev spaces

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83616

Title: Small solutions to nonlinear wave equations in the Sobolev spaces
Authors: Nakamura, N. Browse this author
Ozawa, T. Browse this author
Issue Date: 1-Aug-1999
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 470
Start Page: 1
End Page: 27
Abstract: The local and global well-posedness for the Cauchy problem for a class of nonlinear wave equations is studied. The global well-posedness of the problem is proved in the homogeneous Sobolev space jp = il8(Rn) of fractional order s > n/2 under the following assump­tions: (1} Concerning the Cauchy data (</>,'l/;) E if.s = jJs E9 jJs-1, ll(</>,'l/;);if.11211 is relatively small with respect to 11(</>,'l/;);if.a ll for any fixed a with n/2 < a s; s. (2) Concerning the nonlinearity f, f(u) behaves as a conformal power u1+4/(n-l) near zero and has an arbitrary growth rate at infinity.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69220
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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