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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2025-12-01
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| Series: | Applied Mathematics in Science and Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2025.2522058 |
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| Summary: | 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. |
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| ISSN: | 2769-0911 |