The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations
DOI10.1016/j.camwa.2022.10.021zbMath1504.65193arXiv2204.06060OpenAlexW4308529979WikidataQ115580674 ScholiaQ115580674MaRDI QIDQ2107200
Trung Truong, Dinh-Liem Nguyen, Loc Hoang Nguyen
Publication date: 1 December 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.06060
contraction principlenonlinear hyperbolic equationsCarleman estimatecoefficient inverse problemnumerical reconstruction
Second-order nonlinear hyperbolic equations (35L70) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
- Globally strongly convex cost functional for a coefficient inverse problem
- Numerical computation of the inverse Born approximation for the nonlinear Schrödinger equation in two dimensions
- Functional analysis, Sobolev spaces and partial differential equations
- The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
- Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
- A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
- The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations
- A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem
- Convexification of a 3-D coefficient inverse scattering problem
- A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements
- The Calderón problem for quasilinear elliptic equations
- Convexification of restricted Dirichlet-to-Neumann map
- UNIQUENESS OF RECOVERY OF SOME QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS
- Convexification for a Three-Dimensional Inverse Scattering Problem with the Moving Point Source
- Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs
- A uniqueness theorem and reconstruction of singularities for a two-dimensional nonlinear Schrödinger equation
- Recovering an obstacle and a nonlinear conductivity from Cauchy data
- Newton-Kantorovich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data
- Uniform Strict Convexity of a Cost Functional for Three-Dimensional Inverse Scattering Problem
- Global Convexity in a Three-Dimensional Inverse Acoustic Problem
- Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data
- Convergent Algorithm Based on Carleman Estimates for the Recovery of a Potential in the Wave Equation
- Carleman-Based Reconstruction Algorithm for Waves
- Convexification and experimental data for a 3D inverse scattering problem with the moving point source
- Numerical Solution of a Linearized Travel Time Tomography Problem With Incomplete Data
- An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data
- The fixed angle scattering problem and wave equation inverse problems with two measurements
- Convexification for the Inversion of a Time Dependent Wave Front in a Heterogeneous Medium
- Inverse problems for quadratic derivative nonlinear wave equations
- Convexification numerical algorithm for a 2D inverse scattering problem with backscatter data
This page was built for publication: The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations
