A Quasi-Boundary-Value method for a Cauchy problem of an elliptic equation in multiple dimensions

DOI10.1080/17415977.2013.850683zbMath1321.65165OpenAlexW2002344869MaRDI QIDQ2948537

Wantao Ning, Xiao-Li Feng, Zhi Qian

Publication date: 1 October 2015

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2013.850683

zbMATH Keywords

error estimateelliptic equationvariable coefficientsmultiple dimensionsquasi-boundary-value method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Ill-posed problems for PDEs (35R25) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (12)

Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation ⋮ The quasi-boundary value method for identifying the initial value of the space-time fractional diffusion equation ⋮ A non-homogeneous cauchy problem for an elliptic equation with non-constant coefficient ⋮ Generalized Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation ⋮ Cauchy problem for a semilinear elliptic equation with contaminated coefficients ⋮ Filter regularization method for a time-fractional inverse advection-dispersion problem ⋮ Numerical methods for the forward and backward problems of a time-space fractional diffusion equation ⋮ On a final value problem for the time-fractional diffusion equation with inhomogeneous source ⋮ Unnamed Item ⋮ Regularized solution of the Cauchy problem for the biharmonic equation ⋮ Modified boundary Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation ⋮ Generalized Lavrentiev-type regularization method for the Cauchy problem of a semi-linear elliptic equation

Cites Work

• Unnamed Item
• Unnamed Item
• Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation
• On the inverse potential problem of electrocardiology
• Regularization of ill-posed differential problems
• A new wavelet method for solving an ill-posed problem
• Funktionentheoretische Bestimmung des Außenfeldes zu einer zweidimensionalen magnetohydrostatischen Konfiguration
• Wavelets and regularization of the Cauchy problem for the Laplace equation
• Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
• A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case
• Stability results for a Cauchy problem for an elliptic equation
• Regularization of parabolic equations backward in time by a non-local boundary value problem method
• A non-local boundary value problem method for the Cauchy problem for elliptic equations
• The stability for the Cauchy problem for elliptic equations
• A comparison of regularizations for an ill-posed problem
• Stable determination of a crack from boundary measurements
• On a sideways parabolic equation
• Stability results for the Cauchy problem for the Laplace equation in a strip
• Wavelet and Fourier Methods for Solving the Sideways Heat Equation
• Fourier regularization method for solving a Cauchy problem for the Laplace equation
• Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
• Regularization strategies for a two-dimensional inverse heat conduction problem
• A statistical approach to the Cauchy problem for the Laplace equation
• Inverse problems for partial differential equations

This page was built for publication: A Quasi-Boundary-Value method for a Cauchy problem of an elliptic equation in multiple dimensions