From the 1 of 18 linked papers with an AI index.
18 papers
Global exponential turnpike properties for optimal control of the viscous Burgers equation
Emmanuel Trélat, Xingwu Zeng, Can Zhang
The paper proves that optimal solutions of quadratic tracking problems for the one‑dimensional viscous Burgers equation with localized internal control converge exponentially to a…
Turnpike in optimal control and beyond: a survey
Emmanuel Trélat, Enrique Zuazua
The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide class of long-horizon optimal control problems, the optimal trajectory spends mos…
Weyl asymptotics for singular metrics with a variable boundary degeneracy exponent
Yves Colin de Verdière, Charlotte Dietze, Emmanuel Trélat
We consider a compact smooth manifold of dimension with boundary . In a collar neighborhood of , we assume that the metric has the form …
Moving localized observations and Ces{Ã }ro asymptotic observability for conservative PDEs
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We develop a deterministic large-time mechanism yielding Ces{Ã }ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each obs…
Boundary observability for gas giant metrics
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We study the observability of waves on gas giant manifolds which are a class of Riemannian manifolds whose metrics are singular at the boundary. Such manifolds arise naturally in m…
From PDEs on standard domains to self-similar particle systems on fractals
Georgi Medvedev, Emmanuel Trélat
We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems tha…