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arXiv · 2602.21358

Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks

Elaine A. Tavares-Lima·Bianca Lorenzi·Marcone C. Pereira
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Abstract

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.

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Elaine A. Tavares-Lima, Bianca Lorenzi, Marcone C. Pereira. 2026-02-24. Attractor Continuity for Semilinear Parabolic Equations on Thin Domains with Degenerating Outward Peaks. https://arxiv.org/abs/2602.21358

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