On a structural acoustic model with logarithmic supercritical source terms
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913172043071488 |
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| author | Feng, Baowei Guo, Yanqiu Rammaha, Mohammad A. |
| author_facet | Feng, Baowei Guo, Yanqiu Rammaha, Mohammad A. |
| contents | In this paper, we study a structural acoustic model consisting of a semilinear wave equation defined on a three-dimensional bounded domain, coupled with a Kirchhoff-Love plate equation acting on a flat portion of the boundary. Primarily for mathematical interest, we impose nonlinear damping terms and logarithmic-type supercritical source terms on the system. We investigate local and global well-posedness, energy decay rates of potential well solutions, and blow-up of solutions under different conditions on the parameters and initial data. The main novelties include the analysis of the interaction between nonlinear damping and logarithmic energy-amplifying source terms, as well as the development of techniques for handling logarithmic source terms within potential well theory. The logarithmic nonlinearities are not homogeneous under scaling, which creates difficulties in studying potential well solutions. The wave-plate coupling through the acoustic pressure also causes technical difficulties in the analysis, especially in the proof of blow-up of weak solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a structural acoustic model with logarithmic supercritical source terms Feng, Baowei Guo, Yanqiu Rammaha, Mohammad A. Analysis of PDEs 35L70, 35L75, 35B44, 35B40 In this paper, we study a structural acoustic model consisting of a semilinear wave equation defined on a three-dimensional bounded domain, coupled with a Kirchhoff-Love plate equation acting on a flat portion of the boundary. Primarily for mathematical interest, we impose nonlinear damping terms and logarithmic-type supercritical source terms on the system. We investigate local and global well-posedness, energy decay rates of potential well solutions, and blow-up of solutions under different conditions on the parameters and initial data. The main novelties include the analysis of the interaction between nonlinear damping and logarithmic energy-amplifying source terms, as well as the development of techniques for handling logarithmic source terms within potential well theory. The logarithmic nonlinearities are not homogeneous under scaling, which creates difficulties in studying potential well solutions. The wave-plate coupling through the acoustic pressure also causes technical difficulties in the analysis, especially in the proof of blow-up of weak solutions. |
| title | On a structural acoustic model with logarithmic supercritical source terms |
| topic | Analysis of PDEs 35L70, 35L75, 35B44, 35B40 |
| url | https://arxiv.org/abs/2605.30681 |