Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
From MaRDI portal
Publication:2520118
DOI10.1515/jiip-2016-0039zbMath1351.35263arXiv1603.00848OpenAlexW2963153509MaRDI QIDQ2520118
Nikolaj A. Koshev, Jingzhi Li, Michael V. Klibanov, Anatoly G. Yagola
Publication date: 13 December 2016
Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.00848
Related Items (12)
Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs ⋮ Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data ⋮ FEM-based scalp-to-cortex EEG data mapping via the solution of the Cauchy problem ⋮ Convexification for an inverse parabolic problem ⋮ Convexification of a 3-D coefficient inverse scattering problem ⋮ Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data ⋮ Use of asymptotic analysis for solving the inverse problem of source parameters determination of nitrogen oxide emission in the atmosphere ⋮ A new Fourier truncated regularization method for semilinear backward parabolic problems ⋮ A comparative analysis of numerical methods of solving the continuation problem for 1D parabolic equation with the data given on the part of the boundary ⋮ A new version of the convexification method for a 1D coefficient inverse problem with experimental data ⋮ Convergent numerical methods for parabolic equations with reversed time via a new Carleman estimate ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
- Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems
- Globally strongly convex cost functional for a coefficient inverse problem
- A quasi-reversibility approach to solve the inverse obstacle problem
- Carleman estimates and applications to inverse problems
- Global uniqueness and stability in determining the electric potential coefficient of an inverse problem for Schrödinger equations on Riemannian manifolds
- Carleman estimates for coefficient inverse problems and numerical applications.
- Inverse and ill-posed problems. Theory and applications.
- Calculation of the heat flux near the liquid-gas-solid contact line
- Carleman estimates for the regularization of ill-posed Cauchy problems
- Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data
- Global Lipschitz stability in an inverse hyperbolic problem by interior observations
- GLOBAL UNIQUENESS AND STABILITY IN DETERMINING COEFFICIENTS OF WAVE EQUATIONS
- Iterative methods for an inverse heat conduction problem
- Globally strictly convex cost functional for an inverse parabolic problem
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
- Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
- Solution of nonlinear Cauchy problem for hyperelastic solids
- Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs
- Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets
- Carleman estimates for parabolic equations and applications
- Global Convexity in a Three-Dimensional Inverse Acoustic Problem
- Wavelet and Fourier Methods for Solving the Sideways Heat Equation
- The Cauchy problem for Laplace's equation via the conjugate gradient method
- Optimizational method for solving the Cauchy problem for an elliptic equation
- Numerical solution of the sideways heat equation by difference approximation in time
- Recovering Dielectric Constants of Explosives via a Globally Strictly Convex Cost Functional
- An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
- Inverse problems for partial differential equations
This page was built for publication: Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
