Book contents
- Frontmatter
- Contents
- Preface
- List of Contributors Present at the Summer School
- 1 Controllability of Parabolic Systems: The Moment Method
- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization
- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control
- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations
- 5 About Least-Squares Type Approach to Address Direct and Controllability Problems
- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay
- 7 Ill-Posedness of Coupled Systems with Delay
- 8 Controllability of Parabolic Equations by the Flatness Approach
- 9 Mixing for the Burgers Equation Driven by a Localized Two-Dimensional Stochastic Forcing
- References
1 - Controllability of Parabolic Systems: The Moment Method
Published online by Cambridge University Press: 25 October 2017
Book contents
- Frontmatter
- Contents
- Preface
- List of Contributors Present at the Summer School
- 1 Controllability of Parabolic Systems: The Moment Method
- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization
- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control
- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations
- 5 About Least-Squares Type Approach to Address Direct and Controllability Problems
- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay
- 7 Ill-Posedness of Coupled Systems with Delay
- 8 Controllability of Parabolic Equations by the Flatness Approach
- 9 Mixing for the Burgers Equation Driven by a Localized Two-Dimensional Stochastic Forcing
- References
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- Information
- Evolution EquationsLong Time Behavior and Control, pp. 1 - 30Publisher: Cambridge University PressPrint publication year: 2017
References
[1] , , Indirect controllability of locally coupled wave-type systems and applications,
J. Math. Pures Appl. (9)
99 (2013), no. 5, 544–76.Google Scholar
[2] , , , Null-controllability of some reaction-diffusion systems with one control force, J. Math. Anal. Appl.
320 (2006), no. 2, 928–43.Google Scholar
[3] , , , , The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials,
J. Math. Pures Appl.
96 (2011), no. 6, 555–90.Google Scholar
[4] , , , . Minimal time for the null controllability of parabolic systems: The effect of the condensation index of complex sequences.
J. Funct. Anal.
267 (2014), no. 7, 2077–151.Google Scholar
[5] , , , , New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence. https://hal.archives-ouvertes.fr/hal-01165713, (2015).
[6] , , , Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary,
SIAM J. Control Optim.
30 (1992), no. 5, 1024–65.Google Scholar
[7] , Leçons sur les Progrès Récents de la Théorie des Séries de Dirichlet,
Gauthier-Villars, Paris, (1933).
[8] , , Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients,
Math. Control Relat. Fields
4 (2014), no. 3, 263–87.Google Scholar
[9] .
Control and Nonlinearity,
Mathematical Surveys and Monographs, 136, American Mathematical Society, Providence, RI, (2007).
[10] , , Exact controllability theorems for linear parabolic equations in one space dimension,
Arch. Rational Mech. Anal.
43 (1971), 272–92.Google Scholar
[11] , , Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations,
Quart. Appl. Math.
32
1974/5), 45–69.Google Scholar
[12] , . Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, 34.
Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, (1996).
[13] , , Controllability results for cascade systems of m coupled parabolic PDEs by one control force, Port. Math.
67 (2010), no. 1, 91–113.Google Scholar
[14] .
Analytic Function Theory
. Vol. II. Second edition. AMS Chelsea Publishing, Boston, MA, (2000).
[15] , Sur une expression simple du reste dans la formule d'interpolation de Newton,
Bull. Acad. Roy. Danemark
1894 (1894), 246–52.Google Scholar
[16] , , Contrôle exact de l’équation de la chaleur, Comm. Partial Diff. Eq.
20 (1995), no. 1–2, 335–56.Google Scholar
[17] , Overconvergence of Dirichlet series with complex exponents,
J. Analyse Math
22 (1969), 135–70.Google Scholar
[18] .
Étude des Sommes d'Exponentielles Réelles
. Hermann, Paris, France, 1943.