Averaged dynamics and control for heat equations with random diffusion

[1]  Enrique Zuazua,et al.  On the Controllability of a Fractional Order Parabolic Equation , 2006, SIAM J. Control. Optim..

[2]  G. Lebeau,et al.  Contróle Exact De Léquation De La Chaleur , 1995 .

[3]  G. Tenenbaum,et al.  New blow-up rates for fast controls of Schrödinger and heat equations , 2007 .

[4]  Umberto Biccari,et al.  Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects , 2018, IMA J. Math. Control. Inf..

[5]  Enrique Zuazua,et al.  The cost of approximate controllability for heat equations: the linear case , 2000, Advances in Differential Equations.

[6]  É. Borel.  Sur les zéros des fonctions entières , 1897 .

[7]  D. L. Russell,et al.  Exact controllability theorems for linear parabolic equations in one space dimension , 1971 .

[8]  Enrique Zuazua,et al.  Sharp Observability Estimates for Heat Equations , 2011 .

[9]  Kim Dang Phung,et al.  An observability estimate for parabolic equations from a measurable set in time and its applications , 2013 .

[10]  Luc Miller,et al.  Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time , 2003, math/0307158.

[11]  Bahman Gharesifard,et al.  On average controllability of random heat equations with arbitrarily distributed diffusivity , 2019, Autom..

[12]  Jesús Martínez-Frutos,et al.  Robust Averaged Control of Vibrations for the Bernoulli–Euler Beam Equation , 2017, J. Optim. Theory Appl..

[13]  Luc Miller,et al.  On the Controllability of Anomalous Diffusions Generated by the Fractional Laplacian , 2006, Math. Control. Signals Syst..

[14]  Carlos Castro,et al.  Numerical approximation of the averaged controllability for the wave equation with unknown velocity of propagation , 2021, ESAIM: Control, Optimisation and Calculus of Variations.

[15]  Arnaud Münch,et al.  Strong convergent approximations of null controls for the 1D heat equation , 2013 .

[16]  Enrique Zuazua,et al.  Averaged control , 2014, Autom..

[17]  Jon Asier Bárcena-Petisco.  Null controllability of the heat equation in pseudo-cylinders by an internal control , 2020 .

[18]  Can Zhang,et al.  Analyticity of Solutions to Parabolic Evolutions and Applications , 2015, SIAM J. Math. Anal..

[19]  Enrique Zuazua,et al.  Averaged control and observation of parameter-depending wave equations , 2014 .

[20]  Jean-Michel Coron,et al.  Singular optimal control: A linear 1-D parabolic-hyperbolic example , 2005 .

[21]  E. Zuazua,et al.  Local Elliptic Regularity for the Dirichlet Fractional Laplacian , 2017, 1704.07560.

[22]  Enrique Zuazua,et al.  Numerical approximation of null controls for the heat equation: Ill-posedness and remedies , 2010 .

[23]  E. Zuazua,et al.  Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data , 2014, Archive for Rational Mechanics and Analysis.

[24]  Enrique Zuazua.  Stable observation of additive superpositions of Partial Differential Equations , 2016, Syst. Control. Lett..

[25]  Victor Ivrii,et al.  100 years of Weyl’s law , 2016, Microlocal Analysis, Sharp Spectral Asymptotics and Applications V.

[26]  G. Lebeau,et al.  Spectral inequality and optimal cost of controllability for the Stokes system , 2016 .

[27]  R. Glowinski,et al.  Exact and approximate controllability for distributed parameter systems , 1995, Acta Numerica.

[28]  Luc Miller.  A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups , 2010 .

[29]  Enrique Zuazua,et al.  Averaged controllability for random evolution Partial Differential Equations , 2015, Journal de Mathématiques Pures et Appliquées.

[30]  Luc Miller.  The Control Transmutation Method and the Cost of Fast Controls , 2006, SIAM J. Control. Optim..

[31]  A LOWER BOUND ON LOCAL ENERGY OF PARTIAL SUM OF EIGENFUNCTIONS FOR LAPLACE-BELTRAMI OPERATORS , 2013 .

[32]  J. Apraiz,et al.  Observability Inequalities and Measurable Sets , 2012, 1202.4876.

[33]  Enrique Zuazua,et al.  Averaged controllability of parameter dependent conservative semigroups , 2017 .