Search results for " 35Q61"

showing 2 items of 2 documents

Partial data inverse problems for Maxwell equations via Carleman estimates

2015

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.

Inverse problemsELECTRODYNAMICSINFORMATIONadmissible manifoldsWEIGHTSMathematics::Analysis of PDEsBoundary (topology)InverseBOUNDARY-VALUE PROBLEMCALDERON PROBLEMpartial data01 natural sciencesMATERIAL PARAMETERSinversio-ongelmatsymbols.namesakeMathematics - Analysis of PDEsFOS: Mathematics35R30 35Q61111 MathematicsMaxwellin yhtälötBoundary value problemUniqueness0101 mathematicsPartial dataMathematical PhysicsMathematicsAdmissible manifoldsApplied Mathematicsta111010102 general mathematicsMathematical analysisScalar (physics)Inverse problemCarleman estimatesSmall set010101 applied mathematicsUNIQUENESSMaxwell's equationsMaxwell equationsLOCAL DATAsymbolsAnalysisAnalysis of PDEs (math.AP)
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Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Mathematical optimizationControl and OptimizationMathematicsofComputing_NUMERICALANALYSISFinite element approximations010103 numerical & computational mathematicsType (model theory)01 natural sciencesparabolic time-periodic optimal control problemsError analysisFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisNumerical testsfunctional a posteriori error estimates0101 mathematicsMathematics - Optimization and Control49N20 35Q61 65M60 65F08Mathematicsta113Time periodicta111Numerical Analysis (math.NA)State (functional analysis)Optimal controlComputer Science Applications010101 applied mathematicsOptimization and Control (math.OC)multiharmonic finite element methodsSignal ProcessingA priori and a posterioriAnalysisNumerical Functional Analysis and Optimization
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