On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint
In this paper, we have undertaken the challenging and novel task of establishing the existence of weak solutions for four types of hyperbolic Kirchhoff-type problems: the classical hyperbolic Kirchhoff problem, the problem with a free boundary, the problem with a volume constraint, and the problem c...
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MDPI AG
2025-04-01
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| author | Fatima Ezahra Bentata Ievgen Zaitsev Kamel Saoudi Vladislav Kuchanskyy |
| author_facet | Fatima Ezahra Bentata Ievgen Zaitsev Kamel Saoudi Vladislav Kuchanskyy |
| author_sort | Fatima Ezahra Bentata |
| collection | DOAJ |
| description | In this paper, we have undertaken the challenging and novel task of establishing the existence of weak solutions for four types of hyperbolic Kirchhoff-type problems: the classical hyperbolic Kirchhoff problem, the problem with a free boundary, the problem with a volume constraint, and the problem combining both a volume constraint and a free boundary. These problems are characterized by the presence of non-local terms arising from the Kirchhoff term, the free boundary, and the volume constraint, which introduces significant analytical complexities. To address these challenges, we utilize the discrete Morse flow (DMF) approach, reformulating the original continuous problem into a sequence of discrete minimization problems. This method guarantees the existence of a minimizer for the discretized functional, which subsequently serves as a weak solution to the primary problem. |
| format | Article |
| id | doaj-art-0425417d397945468cd41cc6d8dac8ce |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-0425417d397945468cd41cc6d8dac8ce2025-08-20T02:28:15ZengMDPI AGMathematics2227-73902025-04-01138124310.3390/math13081243On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume ConstraintFatima Ezahra Bentata0Ievgen Zaitsev1Kamel Saoudi2Vladislav Kuchanskyy3Department of Mathematics, Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University-Tebessa, Tebessa 12002, AlgeriaDepartment of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Beresteyskiy Avenue, 56, 03057 Kyiv, UkraineCollege of Sciences at Dammam, University of Imam Abdulrahman Bin Faisal, Dammam 31441, Saudi ArabiaDepartment of Power-Supply Systems Optimization, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Beresteyskiy Avenue, 56, 03057 Kyiv, UkraineIn this paper, we have undertaken the challenging and novel task of establishing the existence of weak solutions for four types of hyperbolic Kirchhoff-type problems: the classical hyperbolic Kirchhoff problem, the problem with a free boundary, the problem with a volume constraint, and the problem combining both a volume constraint and a free boundary. These problems are characterized by the presence of non-local terms arising from the Kirchhoff term, the free boundary, and the volume constraint, which introduces significant analytical complexities. To address these challenges, we utilize the discrete Morse flow (DMF) approach, reformulating the original continuous problem into a sequence of discrete minimization problems. This method guarantees the existence of a minimizer for the discretized functional, which subsequently serves as a weak solution to the primary problem.https://www.mdpi.com/2227-7390/13/8/1243Hyperbolic Kirchhoff-type problemvolume constraintfree boundaryweak solutiondiscrete Morse flow |
| spellingShingle | Fatima Ezahra Bentata Ievgen Zaitsev Kamel Saoudi Vladislav Kuchanskyy On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint Mathematics Hyperbolic Kirchhoff-type problem volume constraint free boundary weak solution discrete Morse flow |
| title | On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint |
| title_full | On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint |
| title_fullStr | On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint |
| title_full_unstemmed | On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint |
| title_short | On Construction of Solutions of Hyperbolic Kirchhoff-Type Problems Involving Free Boundary and Volume Constraint |
| title_sort | on construction of solutions of hyperbolic kirchhoff type problems involving free boundary and volume constraint |
| topic | Hyperbolic Kirchhoff-type problem volume constraint free boundary weak solution discrete Morse flow |
| url | https://www.mdpi.com/2227-7390/13/8/1243 |
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