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