Generalized Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation
DOI10.1007/s11075-018-0573-4zbMath1442.65331OpenAlexW2884463278WikidataQ129413094 ScholiaQ129413094MaRDI QIDQ2424029
Publication date: 21 June 2019
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-018-0573-4
Cauchy problemill-posed problemsemi-linear elliptic equationconvergence estimategeneralized Tikhonov-type regularization method
Stability in context of PDEs (35B35) Spectral theory and eigenvalue problems for partial differential equations (35P99) Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Semilinear elliptic equations (35J61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Analysis and numerical simulation of the three-dimensional Cauchy problem for quasi-linear elliptic equations
- A note on a Cauchy problem for the Laplace equation: Regularization and error estimates
- A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source
- A nonlinear parabolic equation backward in time: regularization with new error estimates
- Boundary-value problem for the two-dimensional elliptic sine-Gordon equation and its application to the theory of the stationary Josephson effect
- A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source
- The Cauchy problem of coupled elliptic sine-Gordon equations with noise: analysis of a general kernel-based regularization and reliable tools of computing
- On an inverse boundary value problem of a nonlinear elliptic equation in three dimensions
- Optimal stable solution of Cauchy problems for elliptic equations
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Modified boundary Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation
- The Dirichlet-to-Neumann map for the elliptic sine-Gordon equation
- A Quasi-Boundary-Value method for a Cauchy problem of an elliptic equation in multiple dimensions
- Why is the Cauchy problem severely ill-posed?
- Approximation of mild solutions of the linear and nonlinear elliptic equations
- A non-local boundary value problem method for the Cauchy problem for elliptic equations
- Inverse problems for partial differential equations
- An introduction to the mathematical theory of inverse problems
This page was built for publication: Generalized Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation
