Article
| Title: | Notes on number of one-troughed travelling waves in asymmetrically supported bending beam (English) |
| Author: | Formánková Levá, Hana |
| Author: | Holubová, Gabriela |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 457-472 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | beam equation |
| Keyword: | jumping nonlinearity |
| Keyword: | travelling wave |
| Keyword: | one-troughed solution |
| MSC: | 34B15 |
| MSC: | 34B40 |
| MSC: | 35A02 |
| MSC: | 35C07 |
| DOI: | 10.21136/AM.2025.0035-25 |
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| Date available: | 2025-10-03T09:11:42Z |
| Last updated: | 2025-10-06 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153087 |
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