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Hokkaido University Preprint Series in Mathematics >
Small solutions to nonlinear wave equations in the Sobolev spaces
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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