Continuity of Global Attractors under a Mass-Preserving Singular Memory Limit, with an Application to a Coupled Suspension Bridge System
Abstract
We study how the global attractor of a dissipative evolution equation with memory depends on the memory kernel when the kernel concentrates, while preserving its total mass, towards a Dirac mass at the origin. The mass-preserving rescaling is the structural feature that prevents the effective elastic coefficients from degenerating in the limit, so that the memory-dependent dynamics reduces formally to a memoryless damped system with unchanged elastic coefficients. For a coupled nonlinear suspension bridge system with past history, taken as a concrete model, we establish uniform-in-parameter dissipativity and uniform-in-parameter exponential stability of the associated linear semigroup. These uniform estimates yield uniform quasi-stability, uniform exponential attraction, finite-time convergence of the semigroups, and uniform Hölder continuity with respect to the perturbation parameter. We deduce upper semicontinuity of the global attractors, and, under an additional structural stability hypothesis on the limit attractor, lower semicontinuity as well. The analysis separates the general continuity mechanism, which applies to a broad class of memory kernels and dissipative systems, from the model-specific verification, which exploits the coupled bridge structure.
Related
- Uniform Exponential Attractors for Non-Autonomous Dynamical Systems and an Application to the damped hyperbolic equation with sub-quintic growth
- A Structure-Preserving LOBPCG Method for Computing Several of the Largest Generalized Singular Triplets
- An energy stable and accuracy-preserving finite volume scheme based on the SAV method with application to wall-distance computation
- GradAgent: A Knowledge-Guided Multi-Agent System for Structure-Preserving Gradient-Flow Computation with an Application to Multicomponent Vesicle Dynamics
- The Oriented Freudenthal Suspension Theorem
BibTeX
@misc{zhou2026continuity,
title = {{Continuity of Global Attractors under a Mass-Preserving Singular Memory Limit, with an Application to a Coupled Suspension Bridge System}},
author = {Jun Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01388},
eprint = {2611.01388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01388},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuity of Global Attractors under a Mass-Preserving Singular Memory Limit, with an Application to a Coupled Suspension Bridge System
AU - Jun Zhou
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01388
UR - https://arxiv.org/abs/2611.01388
AB - We study how the global attractor of a dissipative evolution equation with memory depends on the memory kernel when the kernel concentrates, while preserving its total mass, towards a Dirac mass at the origin. The mass-preserving rescaling is the structural feature that prevents the effective elastic coefficients from degenerating in the limit, so that the memory-dependent dynamics reduces formally to a memoryless damped system with unchanged elastic coefficients. For a coupled nonlinear suspension bridge system with past history, taken as a concrete model, we establish uniform-in-parameter dissipativity and uniform-in-parameter exponential stability of the associated linear semigroup. These uniform estimates yield uniform quasi-stability, uniform exponential attraction, finite-time convergence of the semigroups, and uniform Hölder continuity with respect to the perturbation parameter. We deduce upper semicontinuity of the global attractors, and, under an additional structural stability hypothesis on the limit attractor, lower semicontinuity as well. The analysis separates the general continuity mechanism, which applies to a broad class of memory kernels and dissipative systems, from the model-specific verification, which exploits the coupled bridge structure.
ER -