Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916835632349184 |
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| author | Moumni, Alhabib Pignotti, Cristina Salhi, Jawad Tilioua, Mouhcine |
| author_facet | Moumni, Alhabib Pignotti, Cristina Salhi, Jawad Tilioua, Mouhcine |
| contents | This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other experiences a discrete time delay. By reformulating the problem in an abstract framework, we use semigroup theory and energy methods to establish well-posedness and derive conditions that guarantee exponential energy decay. In the second case, we examine a scenario where a frictional damping term appears in the first equation, while the second equation contains an indefinite damping term, namely with a sign-changing coefficient. Although this setup can be viewed as a special case of the first, we analyze it separately and show that exponential stability still holds under a weaker condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping Moumni, Alhabib Pignotti, Cristina Salhi, Jawad Tilioua, Mouhcine Analysis of PDEs 93B07, 35L05, 93D15, 93C20 This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other experiences a discrete time delay. By reformulating the problem in an abstract framework, we use semigroup theory and energy methods to establish well-posedness and derive conditions that guarantee exponential energy decay. In the second case, we examine a scenario where a frictional damping term appears in the first equation, while the second equation contains an indefinite damping term, namely with a sign-changing coefficient. Although this setup can be viewed as a special case of the first, we analyze it separately and show that exponential stability still holds under a weaker condition. |
| title | Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping |
| topic | Analysis of PDEs 93B07, 35L05, 93D15, 93C20 |
| url | https://arxiv.org/abs/2507.07311 |