Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909523316310016 |
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| author | Haruyama, Yuki Sasaki, Takiko Takamura, Hiroyuki |
| author_facet | Haruyama, Yuki Sasaki, Takiko Takamura, Hiroyuki |
| contents | This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence of classical solutions of semilinear wave equations in one space dimension, especially with derivative nonlinear terms of product-type. Our result is an extension of the single component case, but it is meaningful to provide models as possible as many to cover the optimality of the general theory. The proof is based on the classical iteration argument of the point-wise estimate of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation Haruyama, Yuki Sasaki, Takiko Takamura, Hiroyuki Analysis of PDEs primary 35L71, secondary 35B44 This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence of classical solutions of semilinear wave equations in one space dimension, especially with derivative nonlinear terms of product-type. Our result is an extension of the single component case, but it is meaningful to provide models as possible as many to cover the optimality of the general theory. The proof is based on the classical iteration argument of the point-wise estimate of the solution. |
| title | Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation |
| topic | Analysis of PDEs primary 35L71, secondary 35B44 |
| url | https://arxiv.org/abs/2409.06378 |