Insensitizing controls for a semilinear heat equation

By Luz de Teresa. 2000

160 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/ff566fe8b8cb52190c91d2986be0ee4f484ab153

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In Computational Theory and Mathematics

In Control and Systems Engineering

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Citations in the corpus

Controllability results for cascade systems of m coupled parabolic PDEs by one control force (2010, unknown): “In [19] and [5] the authors consider a nonlinear system of two heat equations, one of them being forward and the other one”
Existence of Insensitizing Controls for a Semilinear Heat Equation with a Superlinear Nonlinearity (2004, methodology): “At present both problems are far from being solved for disjoint control set and observation set (see De Teresa, 2000).”
A GENERALIZATION OF THE KALMAN RANK CONDITION FOR TIME-DEPENDENT COUPLED LINEAR PARABOLIC SYSTEMS (2009, background): “In [18], [5] and [13] the authors consider linear and nonlinear systems of two heat equations, one of them being forward and the other one backward in time, and show the null controllability of the considered systems.”
New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence (2016, background): “The first results on controllability of coupled parabolic equations (n > 1) have been established in [35, 13, 3, 25].”
Controllability of systems of Stokes equations with one control force: existence of insensitizing controls (2007, unknown): “In [3], the author proved the existence of insensitizing controls for the same system.”
Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient (2004, methodology): “The rest of this paper is organized as follows: in section 2, we first prove an observability inequality that generalizes the one in [3].”
INDIRECT STABILIZATION OF LOCALLY COUPLED WAVE-TYPE SYSTEMS (2012, background): “data, is it possible to find a control function f so that the state has been driven to zero in time T? The parabolic null-controllability problem (8) is fully solved in the case ωb ∩ ωp 6= ∅ (see [29, 9, 16, 21]).”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, methodology): “The use of global parabolic Carleman estimates has also allowed to address the controllability of non linear equations such as the Navier-Stokes equations [19,29], the Boussinesq system [20], fluid structure systems [9,30], weakly coupled parabolic systems [12,23,32,33] to cite a few.”
A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems (2009, background): “In order to bound I1 and I2, we will reason as in [21] and [12].”
The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials (2011, background): “In the last ten years, the study of the controllability properties of coupled parabolic systems has had an increasing interest (see for instance [30], [2] [8], [6], [3], [18], [20], [4], [5], [19], [23] and [9]).”
CONTROLLABILITY OF 1-D COUPLED DEGENERATE PARABOLIC EQUATIONS (2009, background): “A more complete analysis of this phenomenon (in the non degenerate case) can be found in [22] and in [23].”
Global Carleman estimate for stochastic parabolic equations, and its application (2014, background): “In [24], the author showed that when G\G0 = ∅, one could not expect the existence of insensitizing controls for every initial value y0 ∈ L(2)(G), even for the linear parabolic equation; while when G0∩O1 = ∅, for y0 = 0 and ξ satisfying suitable assumptions, the existence of insensitizing controls wa”