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dc.contributor.authorCasas, E.
dc.contributor.authorVexler, B.
dc.contributor.authorZuazua, E.
dc.description.abstractWe address the problem of inverse source identication for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a nite number of pointwise locations. Moreover, we discuss the nite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectApproximate controllability
dc.subjectBorel measures
dc.subjectParabolic equations
dc.subjectSparse controls
dc.titleSparse initial data identification for parabolic PDE and its finite element approximations
dc.journal.titleMathematical Control and Related Fieldsen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España