Hernández Salinas, Martín SebastiánZuazua, Enrique2025-04-152025-04-152024-04Hernández, M., & Zuazua, E. (2024). Uniform Turnpike property and singular limits. Acta Applicandae Mathematicae, 190(1). https://doi.org/10.1007/S10440-024-00640-70167-801910.1007/S10440-024-00640-7http://hdl.handle.net/20.500.14454/2625Motivated 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 experimentseng© The Author(s) 2024Long time behaviorOptimal control problemsRapidly oscillating linear parabolic equationSingular limits problemsTurnpike propertyUniform controllabilityjournal article2025-04-151572-9036