Qualitative analysis for a new constrained hyperbolic p-Kirchhoff type problem involving free boundary
Abstract In this work, we investigate the existence of weak solutions for a constrained hyperbolic p-Kirchhoff type problem involving a free boundary. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original problem as a sequence of minimization problems in discrete time int...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02070-2 |
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| Summary: | Abstract In this work, we investigate the existence of weak solutions for a constrained hyperbolic p-Kirchhoff type problem involving a free boundary. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original problem as a sequence of minimization problems in 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, introduced by the p-Kirchhoff term and the volume constraint with a free boundary, poses significant analytical challenges. 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: | 1687-2770 |