Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Tavares-Lima, Elaine A. Lorenzi, Bianca Pereira, Marcone C. |
| author_facet | Tavares-Lima, Elaine A. Lorenzi, Bianca Pereira, Marcone C. |
| contents | In this work, we analyze the asymptotic behavior of the attractors associated with a semilinear parabolic equation subject to homogeneous Neumann boundary conditions and defined on a thin domain $R^\varepsilon \subset \mathbb{R}^{1+n}$. We assume that the thin domain exhibits a cusp, known as an outward peak, whose geometry is characterized by a nonnegative function that vanishes at a point on the boundary. Our objective is to rigorously establish the continuity of the attractors as $\varepsilon \to 0$ and to determine their rate of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks Tavares-Lima, Elaine A. Lorenzi, Bianca Pereira, Marcone C. Analysis of PDEs 35B41, 35K65, 41A25, 37L05 In this work, we analyze the asymptotic behavior of the attractors associated with a semilinear parabolic equation subject to homogeneous Neumann boundary conditions and defined on a thin domain $R^\varepsilon \subset \mathbb{R}^{1+n}$. We assume that the thin domain exhibits a cusp, known as an outward peak, whose geometry is characterized by a nonnegative function that vanishes at a point on the boundary. Our objective is to rigorously establish the continuity of the attractors as $\varepsilon \to 0$ and to determine their rate of convergence. |
| title | Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks |
| topic | Analysis of PDEs 35B41, 35K65, 41A25, 37L05 |
| url | https://arxiv.org/abs/2602.21358 |