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
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
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.
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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