New blow-up rates for fast controls of Schrödinger and heat equations

DOI10.1016/j.jde.2007.06.019zbMath1127.93016OpenAlexW2041959383MaRDI QIDQ2464146

Marius Tucsnak, Gérald Tenenbaum

Publication date: 10 December 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.06.019

zbMATH Keywords

heat equationSchrödinger equationnull-controllabilityseries of exponentials

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Observability (93B07) Control/observation systems in abstract spaces (93C25) Applications of sieve methods (11N36)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Primes in arithmetic progressions to large moduli. II
• Two results on exact boundary control of parabolic equations
• A lower bound of the norm of the control operator for the heat equation
• Admissibility of input elements for diagonal semigroups on \(\ell\) 2
• How violent are fast controls?
• How violent are fast controls? II
• Controllability cost of conservative systems: resolvent condition and transmutation
• Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
• How violent are fast controls for Schrödinger and plate vibrations?
• Control of the Schrödinger equation
• The ``window problem for series of complex exponentials
• Exact controllability theorems for linear parabolic equations in one space dimension
• A spectral approach for the exact observability of infinite-dimensional systems with skew-adjoint generator
• The Control Transmutation Method and the Cost of Fast Controls
• Admissible Input Elements for Systems in Hilbert Space and a Carleson Measure Criterion
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• A General Theory of Observation and Control
• Admissibility of Unbounded Control Operators
• Mathematical control theory: an introduction
• The cost of approximate controllability for heat equations: The linear case

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