Exhaustion approximation for the control problem of the heat or Schrödinger semigroup on unbounded domains

DOI10.1007/s00013-020-01484-xzbMath1442.35488arXiv1810.12167OpenAlexW3035952261MaRDI QIDQ777083

Albrecht Seelmann, Ivan Veselić

Publication date: 3 July 2020

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12167

zbMATH Keywords

heat equationunbounded domaincontrol problemSchrödinger semigroupapproximation exhaustion

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Heat equation (35K05) PDEs in connection with control and optimization (35Q93)

Related Items (6)

The reflection principle in the control problem of the heat equation ⋮ Constrained linear-quadratic optimization problems with parameter-dependent entries ⋮ Observability and null-controllability for parabolic equations in \(L_p\)-spaces ⋮ Sharp estimates and homogenization of the control cost of the heat equation on large domains ⋮ Scale-free unique continuation estimates and Logvinenko-Sereda theorems on the torus ⋮ A uniform bound on costs of controlling semilinear heat equations on a sequence of increasing domains and its application

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounds on the spectral shift function and the density of states
• Semigroups of linear operators and applications to partial differential equations
• Sharp geometric condition for null-controllability of the heat equation on \(\mathbb R^d\) and consistent estimates on the control cost
• Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators
• Dirichlet problems on varying domains.
• Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains
• Observable set, observability, interpolation inequality and spectral inequality for the heat equation in \(\mathbb{R}^n\)
• Schrödinger semigroups
• On the null-controllability of diffusion equations
• Brownian motion and harnack inequality for Schrödinger operators
• CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS
• Null-controllability of hypoelliptic quadratic differential equations
• A diamagnetic inequality for semigroup differences
• Sharp estimates and homogenization of the control cost of the heat equation on large domains

This page was built for publication: Exhaustion approximation for the control problem of the heat or Schrödinger semigroup on unbounded domains