Asymptotic Dynamics and Continuity of Exponential Attractors for a Generalized Nonautonomous Second-Order Equation
Year: 2026
Type: article
Abstract: In this work, we analyze the asymptotic behavior of solutions to a generalized semilinear damped wave equation with time-dependent coefficients, subject to homogeneous Dirichlet boundary conditions on a smooth bounded domain $$\Omega \subset \mathbb {R}^N$$ Ω ⊂ R N , $$N \ge 3$$ N ≥ 3 . The equation involves functions $$\alpha _\epsilon (t)$$ α ϵ ( t ) , $$\beta _\epsilon (t)$$ β ϵ ( t ) , $$\mu _\epsilon (t)$$ μ ϵ ( t ) , and $$\eta _\epsilon (t)$$ η ϵ ( t ) depending continuously on time and on a parameter $$\epsilon \in [0,1]$$ ϵ ∈ [ 0 , 1 ] , and includes a nonlinear term f ( u ) satisfying suitable growth, regularity, and dissipativity assumptions. By means of a time-rescaling argument, we establish the existence of pullback exponential attractors and pullback attractors whose sections possess uniformly bounded finite fractal dimension. Furthermore, we prove the continuity of the family of pullback exponential attractors and the upper semicontinuity of the family of pullback attractors with respect to the parameter $$\epsilon $$ ϵ . These results provide a unified framework for analyzing the robustness and regularity of nonautonomous dissipative dynamics under parameter perturbations.
Institution: Universidade Federal de São Carlos
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7165113307