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^ε ⊂ R¹⁺ⁿ R ε ⊂ 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 ε → 0 ε → 0 and to determine their rate of convergence.