Search results for "increasing stability phenomena"

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Optimality of Increasing Stability for an Inverse Boundary Value Problem

2021

In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger equation were established by Isakov [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and by Isakov et al. [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141]. In [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141], the authors showed that the stability of this IBVP increases …

increasing stability phenomenaosittaisdifferentiaaliyhtälötinstabilityComputational MathematicsMathematics - Analysis of PDEsApplied Mathematics35J15 35R25 35R30FOS: MathematicsSchrödinger equationinverse boundary value probleminversio-ongelmatAnalysisAnalysis of PDEs (math.AP)SIAM Journal on Mathematical Analysis
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Refined instability estimates for some inverse problems

2022

Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache [29]. In this work, based on Mandache's idea, we refine the instability estimates for two inverse problems, including the inverse inclusion problem and the inverse scattering problem. Our aim is to derive explicitly the dependence of the instability estimates on key parameters. The first result of this work is to show how the instability depends on the depth of the hidden inclusion and the conductivity of the background medium. This work can be regarded as a counterpart of the depth-dependent and conductivity-dependent stability estim…

osittaisdifferentiaaliyhtälötimpedanssitomografiascattering theoryControl and Optimizationdepth-dependent instability of exponential-typeinverse problemsinversio-ongelmatincreasing stability phenomenainstabilityCalderón's problem35R30kuvantaminenRellich lemmaModeling and Simulation35J15Discrete Mathematics and CombinatoricssirontaHelmholtz equation35R25Analysiselectrical impedance tomographyInverse Problems and Imaging
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