Controllability and Observability of Partial Differential Equations: Some Results and Open Problems

By Enrique Zuazua. 2007

316 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91657a9d4e15927290008ed5f9125f4154c36905

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Xu Zhang
2. Enrique Zuazua
3. Sylvain Ervedoza
4. Emmanuel Trélat
5. Xiaoyu Fu
6. Qi Lu
7. Jiongmin Yong
8. Mikko Salo

In Control and Systems Engineering

1. Enrique Zuazua
2. Xu Zhang
3. Sylvain Ervedoza
4. Xiaoyu Fu
5. Emmanuel Trélat
6. Qi Lu
7. Jiongmin Yong
8. Angkana Rüland

In Mathematical Physics

1. Xu Zhang
2. Enrique Zuazua
3. Sylvain Ervedoza
4. Qi Lu
5. Angkana Rüland
6. Mikko Salo
7. Emmanuel Trélat
8. Xiaoyu Fu

Citations in the corpus

• Quantitative approximation properties for the fractional heat equation (2017, background): “for instance [11, 13, 27, 25, 31, 32, 33, 41] and in particular [2, 30, 29] for the setting of non-local equations and the references therein), in the present article, motivated by applications to inverse problems, we seek to approximate a given function at each time slice by choosing suitable exter”
• A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA (2010, background): “, on which there is also extensive literature about their controllability properties, see [25].”
• A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, background): “2 has some other applications in control problems of PDEs ([32, 34, 44, 49, 55, 56]).”
• Minimal controllability time for the heat equation under unilateral state or control constraints (2017, background): “The system is well known to be null-controllable in any time T > 0 with controls u ∈ L(2)((0, T )× ∂Ω) (see [7, 12, 28]).”
• Null Controllability for Wave Equations with Memory (2015, background): “Observe that (25) is the usual observability inequality that is assured in the context of wave equations if the GCC is satisfied (see [38] for a discussion of other methods to achieve these observability inequalities for the classical 95 wave equations).”
• Controllability and observability of a heat equation with hyperbolic memory kernel (2009, background): “5) There are numerous studies on observability estimate for partial differential equations (PDEs, for short), mainly for those without memory or at most with “small” memory (see [28] and the rich references cited therein).”
• Sharp Observability Estimates for Heat Equations (2011, background): “Observe also that, as pointed out in [43] and recently further developed in [27], these estimates and their optimality are intimately related with the spectral estimates by Lebeau and Robbiano [22] on the observability of packets of eigenfunctions.”