On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials
By Thomas Duyckaerts, Xu Zhang, Enrique Zuazua. 2008
199 citations recorded by the source corpus.
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/da1d10946d7a6a451af703067f6f2491dd7bf943
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Enrique Zuazua
- Sylvain Ervedoza
- Karine Beauchard
- Xu Zhang
- Luc Miller
- Piermarco Cannarsa
- Morgan Morancey
- Roberto Guglielmi
In Mathematical Physics
- Enrique Zuazua
- Sylvain Ervedoza
- Karine Beauchard
- Xu Zhang
- Piermarco Cannarsa
- Luc Miller
- Morgan Morancey
- Roberto Guglielmi
Citations in the corpus
- Global Carleman Estimates for Waves and Applications (2011, unknown): “AMS subject classifications: 93B07, 93C20, 35R30.”
- A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, methodology): “Concerning the nonlinearity h(·), we need the following assumption ([10]).”
- Sharp estimates and homogenization of the control cost of the heat equation on large domains (2018, unknown): “the limit T → 0 and T → ∞ is optimal as discussed in Remark 2.16, see also Table 1. We also note that the term kV k2/3 ∞ in the bound in Theorem 3.9 is optimal, at least in even space dimensions, see [DZZ08]. Furthermore, the dependence of the rate of the exponential term on the parameter G in Theor”
- 2d Grushin-type equations: Minimal time and null controllable data (2015, methodology): “The use of both a transmutation method and lateral propagation of energy was already suggested in [17] by Duyckaerts, Zhang and Zuazua.”
- The Wave Equation: Control and Numerics (2012, background): “The same problems arise in the context of many other nonlinea r PDE, for instance: semilinear Schrödinger equations [62], KdV equat ions [95], semilinear heat equations [112, 26], etc.”
- Null controllability of Grushin-type operators in dimension two (2011, background): “The optimality of the power 2/3 of A in H(T ,A,B) has been proved in [17].”
- Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, background): “But, as we shall see in the following section, according to the recent results in [50], the estimate turns out to be sharp.”