We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Uniform Turnpike Property and Singular Limits.
- Authors
Hernández, Martín; Zuazua, Enrique
- Abstract
Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments.
- Subjects
RICCATI equation; HEAT equation; ASYMPTOTIC homogenization
- Publication
Acta Applicandae Mathematicae, 2024, Vol 190, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-024-00640-7