Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912951047290880 |
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| author | Wu, Wenlong Zhang, Yanyan |
| author_facet | Wu, Wenlong Zhang, Yanyan |
| contents | This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a positive voltage parameter $λ$. We establish the convergence of global solutions to an equilibrium, along with the convergence rate estimates. Supporting numerical simulations are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions Wu, Wenlong Zhang, Yanyan Analysis of PDEs 35B40, 35K35, 35L70, 74F15, 74H40 This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a positive voltage parameter $λ$. We establish the convergence of global solutions to an equilibrium, along with the convergence rate estimates. Supporting numerical simulations are presented. |
| title | Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions |
| topic | Analysis of PDEs 35B40, 35K35, 35L70, 74F15, 74H40 |
| url | https://arxiv.org/abs/2603.07042 |