Chevron pattern equations: exponential attractor and global stabilization
H. Kalantarova, V. Kalantarov, O. Vantzos
TL;DR
This paper investigates the mathematical modeling of chevron patterns, establishing the existence of exponential attractors and stabilization methods for solutions in both one and two dimensions, supported by theoretical proofs and numerical results.
Contribution
It introduces new stabilization techniques for chevron pattern models and proves the existence of exponential attractors in two dimensions, advancing understanding of pattern control.
Findings
Existence of exponential attractors in two-dimensional models.
Stabilization of zero steady state via finite-dimensional feedback control.
Numerical validation of stabilization methods.
Abstract
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state solution through application of a finite-dimensional feedback control is proved in two spatial dimensions. The stabilization of an arbitrary fixed solution is shown in one spatial dimension along with relevant numerical results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Dynamics and Pattern Formation · Advanced Mathematical Modeling in Engineering