Solvability of interior transmission problem for the diffusion equation by constructing its Green function

DOI10.1515/jiip-2018-0027zbMath1425.35236arXiv1706.04745OpenAlexW2950712732MaRDI QIDQ2010470

Gen Nakamura, Haibing Wang

Publication date: 27 November 2019

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04745

zbMATH Keywords

inverse problemdiffusion equationsolvabilityinterior transmission problem

Mathematics Subject Classification ID

Heat equation (35K05) Inverse problems for PDEs (35R30)

Related Items (3)

Numerical solutions of the forward and inverse problems arising in diffuse optical tomography ⋮ Normalized solutions for an horizontal transmission problem ⋮ Born series for the photon diffusion equation perturbing the Robin boundary condition

Cites Work

• Unnamed Item
• Unnamed Item
• The Green function of the interior transmission problem and its applications
• Numerical solution of an inverse boundary value problem for the heat equation with unknown inclusions
• The interior transmission problem
• On the existence of transmission eigenvalues
• On general boundary value problem for parabolic equations
• An asymptotic expansion for the heat equation
• Inverse Scattering Theory and Transmission Eigenvalues
• Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
• Ellipticity in the Interior Transmission Problem in Anisotropic Media
• Finite Element Methods for Maxwell's Transmission Eigenvalues
• Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues
• The Interior Transmission Problem for Regions with Cavities
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• Reconstruction of an unknown inclusion by thermography
• The Electromagnetic Interior Transmission Problem for Regions with Cavities
• Transmission Eigenvalues for Elliptic Operators
• Iterative Methods for Transmission Eigenvalues
• The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media
• Reconstruction of an unknown cavity with Robin boundary condition inside a heat conductor
• Transmission Eigenvalues
• The Denseness of the Far Field Patterns for the Transmission Problem
• On isotropic cloaking and interior transmission eigenvalue problems
• Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking
• The Interior Transmission Eigenvalue Problem
• Transmission Eigenvalues for Operators with Constant Coefficients
• Inside-Outside Duality and the Determination of Electromagnetic Interior Transmission Eigenvalues
• Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method
• Transmission eigenvalues in one dimension
• Linear sampling method for the heat equation with inclusions
• The Interior Transmission Problem: Spectral Theory
• The Resolvent of an Elliptic Boundary Problem
• Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations

This page was built for publication: Solvability of interior transmission problem for the diffusion equation by constructing its Green function