General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface
In this work, we investigate the existence of weak solutions for the general form of the hyperbolic Kirchhoff-type problem involving a free boundary modelling the free vibration of an elastic string on a flat surface. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original...
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Taylor & Francis Group
2025-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2025.2522058 |
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| author | Fatima Ezahra Bentata Ievgen Zaitsev |
| author_facet | Fatima Ezahra Bentata Ievgen Zaitsev |
| author_sort | Fatima Ezahra Bentata |
| collection | DOAJ |
| description | In this work, we investigate the existence of weak solutions for the general form of the hyperbolic Kirchhoff-type problem involving a free boundary modelling the free vibration of an elastic string on a flat surface. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original problem as a sequence of minimization problems at discrete time intervals. This ensures the existence of a minimizer for the discretized functional, which in turn serves as a weak solution to the main problem. The presence of non-local terms, arising from the p-Kirchhoff term, introduces dependencies on the gradient norm [Formula: see text] across the entire domain, making the analysis more challenging. These non-local terms encapsulate the effect of the free boundary and influence the behaviour of the solution globally, rather than being determined solely by local values of v. Our study provides a rigorous treatment to overcome these difficulties. Furthermore, we present numerical simulations to illustrate the physical implications of our results. |
| format | Article |
| id | doaj-art-7459db0268b44cf4a8f70568a8fcf5c2 |
| institution | DOAJ |
| issn | 2769-0911 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-7459db0268b44cf4a8f70568a8fcf5c22025-08-20T03:18:01ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112025-12-0133110.1080/27690911.2025.2522058General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surfaceFatima Ezahra Bentata0Ievgen Zaitsev1Department of Mathematics, Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University-Tebessa, Tebessa, AlgeriaDepartment of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Kyiv, UkraineIn this work, we investigate the existence of weak solutions for the general form of the hyperbolic Kirchhoff-type problem involving a free boundary modelling the free vibration of an elastic string on a flat surface. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original problem as a sequence of minimization problems at discrete time intervals. This ensures the existence of a minimizer for the discretized functional, which in turn serves as a weak solution to the main problem. The presence of non-local terms, arising from the p-Kirchhoff term, introduces dependencies on the gradient norm [Formula: see text] across the entire domain, making the analysis more challenging. These non-local terms encapsulate the effect of the free boundary and influence the behaviour of the solution globally, rather than being determined solely by local values of v. Our study provides a rigorous treatment to overcome these difficulties. Furthermore, we present numerical simulations to illustrate the physical implications of our results.https://www.tandfonline.com/doi/10.1080/27690911.2025.2522058Hyperbolic p-Kirchhoff type problemfree boundaryweak solutiondiscrete morse flownumerical simulation35M11 |
| spellingShingle | Fatima Ezahra Bentata Ievgen Zaitsev General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface Applied Mathematics in Science and Engineering Hyperbolic p-Kirchhoff type problem free boundary weak solution discrete morse flow numerical simulation 35M11 |
| title | General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface |
| title_full | General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface |
| title_fullStr | General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface |
| title_full_unstemmed | General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface |
| title_short | General hyperbolic Kirchhoff model for the free vibration of elastic string on a flat surface |
| title_sort | general hyperbolic kirchhoff model for the free vibration of elastic string on a flat surface |
| topic | Hyperbolic p-Kirchhoff type problem free boundary weak solution discrete morse flow numerical simulation 35M11 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2025.2522058 |
| work_keys_str_mv | AT fatimaezahrabentata generalhyperbolickirchhoffmodelforthefreevibrationofelasticstringonaflatsurface AT ievgenzaitsev generalhyperbolickirchhoffmodelforthefreevibrationofelasticstringonaflatsurface |