Variational source condition for ill-posed backward nonlinear Maxwell’s equations

DOI10.1088/1361-6420/aaeebezbMath1414.35223OpenAlexW2900170959WikidataQ128980434 ScholiaQ128980434MaRDI QIDQ4646431

De-Han Chen, Irwin Yousept

Publication date: 14 January 2019

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/6f7914849025b1843ad73465fd1a66d7fb1db9ab

zbMATH Keywords

inverse problemsTikhonov regularizationvariational source conditionnonlinear Maxwell's equationsill-posed backward evolution equations

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear ill-posed problems (47J06) Moment problems and interpolation problems in the complex plane (30E05) Electromagnetic theory (general) (78A25) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Linear operators and ill-posed problems, regularization (47A52) Maxwell equations (35Q61)

Related Items (10)

Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems ⋮ Dual gradient method for ill-posed problems using multiple repeated measurement data ⋮ Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems ⋮ Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion ⋮ Variational Source Conditions in $L^p$-spaces ⋮ Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion ⋮ Variational source conditions for inverse Robin and flux problems by partial measurements ⋮ Convergence of a spectral regularization of a time-reversed reaction-diffusion problem with high-order Sobolev-Gevrey smoothness ⋮ Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system ⋮ Oversmoothing Tikhonov regularization in Banach spaces ^*

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