Notes on number of one-troughed travelling waves in asymmetrically supported bending beam
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912869309743104 |
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| author | Levá, Hana Formánková Holubová, Gabriela |
| author_facet | Levá, Hana Formánková Holubová, Gabriela |
| contents | We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions, the so-called one-troughed travelling waves. The main goal of this paper is to show the existence of at least two different one-troughed travelling waves for particular wave speeds and input parameters of the studied problem. We present the upper bounds for the maximal number of one-troughed solutions together with a visualisation of obtained results and corresponding solutions. Finally, we list several open questions regarding this topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on number of one-troughed travelling waves in asymmetrically supported bending beam Levá, Hana Formánková Holubová, Gabriela Analysis of PDEs Classical Analysis and ODEs 35A02, 35C07, 34B15, 34B40 We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions, the so-called one-troughed travelling waves. The main goal of this paper is to show the existence of at least two different one-troughed travelling waves for particular wave speeds and input parameters of the studied problem. We present the upper bounds for the maximal number of one-troughed solutions together with a visualisation of obtained results and corresponding solutions. Finally, we list several open questions regarding this topic. |
| title | Notes on number of one-troughed travelling waves in asymmetrically supported bending beam |
| topic | Analysis of PDEs Classical Analysis and ODEs 35A02, 35C07, 34B15, 34B40 |
| url | https://arxiv.org/abs/2501.07940 |