Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911740841689088 |
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| author | Hamza, Mohamed Ali Wakasugi, Yuta Yoshikawa, Shuji |
| author_facet | Hamza, Mohamed Ali Wakasugi, Yuta Yoshikawa, Shuji |
| contents | In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear case. In contrast to our previous result [6], in which the asymptotic profile is governed by the linear heat kernel and the nonlinear effect is asymptotically negligible, the asymptotic profile in the present setting is described by a self-similar solution to the associated nonlinear parabolic equation (constructed in Brezis-Peletier-Terman [1]). The proof relies on delicate energy estimates in weighted spaces formulated in parabolic self-similar variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case Hamza, Mohamed Ali Wakasugi, Yuta Yoshikawa, Shuji Analysis of PDEs In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear case. In contrast to our previous result [6], in which the asymptotic profile is governed by the linear heat kernel and the nonlinear effect is asymptotically negligible, the asymptotic profile in the present setting is described by a self-similar solution to the associated nonlinear parabolic equation (constructed in Brezis-Peletier-Terman [1]). The proof relies on delicate energy estimates in weighted spaces formulated in parabolic self-similar variables. |
| title | Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.00550 |