Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910742413836288 |
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| author | Sobajima, Motohiro Tsutaya, Kimitoshi Wakasugi, Yuta |
| author_facet | Sobajima, Motohiro Tsutaya, Kimitoshi Wakasugi, Yuta |
| contents | In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data. Our result contains small data blowup for sub-Strauss exponent for the simplest semilinear wave equation and also the one for semilinear generalized Tricomi equation. Key ingredient is so-called test function method (developed in Ikeda--Sobajima--Wakasa [10]) with a certain conservative quantity via a special solution with the Liouville--Green (or WKB) approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation Sobajima, Motohiro Tsutaya, Kimitoshi Wakasugi, Yuta Analysis of PDEs 35L71, 35Q85 In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data. Our result contains small data blowup for sub-Strauss exponent for the simplest semilinear wave equation and also the one for semilinear generalized Tricomi equation. Key ingredient is so-called test function method (developed in Ikeda--Sobajima--Wakasa [10]) with a certain conservative quantity via a special solution with the Liouville--Green (or WKB) approximation. |
| title | Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation |
| topic | Analysis of PDEs 35L71, 35Q85 |
| url | https://arxiv.org/abs/2412.08834 |