Uniform Turnpike Property and Singular Limits

Hernández Salinas M, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Article in Edited Volumes

Publication year: 2024

Journal

Acta Applicandae Mathematicae Springer Verlag (Germany)

Book Volume: 190

Journal Issue: 3

URI: https://link.springer.com/article/10.1007/s10440-024-00640-7

DOI: 10.1007/s10440-024-00640-7

Open Access Link: https://arxiv.org/abs/2308.15257

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.

Authors with CRIS profile

Martin Hernández Salinas Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Hernández Salinas, M., & Zuazua Iriondo, E. (2024). Uniform Turnpike Property and Singular Limits. Acta Applicandae Mathematicae, 190(3). https://doi.org/10.1007/s10440-024-00640-7

MLA:

Hernández Salinas, Martin, and Enrique Zuazua Iriondo. "Uniform Turnpike Property and Singular Limits." Acta Applicandae Mathematicae 190.3 (2024).

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