Source inversion of heat conduction from a finite number of observation data

DOI10.1080/00036810903569523zbMath1197.65132OpenAlexW2083741924WikidataQ58184521 ScholiaQ58184521MaRDI QIDQ3569219

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Publication date: 18 June 2010

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810903569523

zbMATH Keywords

inverse problemheat conductionreproducing kernelTikhonov regularizationgeneralized inversesPaley-Wiener spaceGaussian convolutionWeierstrass transformreproducing-kernel Hilbert spacesreal inversion formulae

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Heat equation (35K05) Inverse problems for PDEs (35R30) Numerical methods for integral transforms (65R10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (3)

General inhomogeneous discrete linear partial differential equations with constant coefficients on the whole spaces ⋮ Optimal and approximate solutions of singular integral equations by means of reproducing kernels ⋮ A fundamental theorem on initial value problems by using the theory of reproducing kernels

Cites Work

• The weierstrass transform and an isometry in the heat equation
• On the Inversion of the Gauss Transformation
• Approximate real inversion formulas of the gaussian convolution
• Approximate and analytical inversion formulas in heat conduction on multidimensional spaces
• Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces
• Dirichlet principle using computers
• A Generalization of an Inversion Formula for the Gauss Transformation

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