Displaying similar documents to “Well posedness and control of semilinear wave equations with iterated logarithms”

Exact controllability of the 1-d wave equation from a moving interior point

Carlos Castro (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.

Exact controllability of the radial solutions of the semilinear wave equation in R.

Luz de Teresa (1998)

Revista Matemática Complutense

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The exact internal controllability of the radial solutions of a semilinear heat equation in R is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.

Numerical controllability of the wave equation through primal methods and Carleman estimates

Nicolae Cîndea, Enrique Fernández-Cara, Arnaud Münch (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible...

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Mark Asch, Marion Darbas, Jean-Baptiste Duval (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion...

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Mark Asch, Marion Darbas, Jean-Baptiste Duval (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion...

Controllability of partial differential equations on graphs

Sergei Avdonin, Victor Mikhaylov (2008)

Applicationes Mathematicae

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We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the...