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08/25/2023
The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients
This paper aims to reconstruct the initial condition of a hyperbolic equ...
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05/31/2023
The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data
The objective of this article is to introduce a novel technique for comp...
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04/12/2023
Numerical differentiation by the polynomial-exponential basis
Our objective is to calculate the derivatives of data corrupted by noise...
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12/23/2022
Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
The first globally convergent numerical method for a Coefficient Inverse...
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10/17/2022
Reconstructing a space-dependent source term via the quasi-reversibility method
The aim of this paper is to solve an important inverse source problem wh...
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06/23/2022
Convexification for a CIP for the RTE]Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation
An ( n+1) -D coefficient inverse problem for the radiative stationary tr...
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06/20/2022
The Carleman convexification method for Hamilton-Jacobi equations on the whole space
We propose a new globally convergent numerical method to solve Hamilton-...
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09/23/2021
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data
It is shown that the contraction mapping principle with the involvement ...
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08/18/2021
A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications
We propose a new iterative scheme to compute the numerical solution to a...
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08/07/2021
Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equation
The main aim of this paper is to solve an inverse source problem for a g...
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04/23/2021
Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data
To compute the spatially distributed dielectric constant from the backsc...
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04/13/2021
Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method
We propose a globally convergent numerical method, called the convexific...
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03/06/2021
The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem
We study the global convergence of the gradient descent method of the mi...
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11/10/2020
The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations
We propose a numerical method to solve an inverse source problem of comp...
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05/29/2020
An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data
This report extends our recent progress in tackling a challenging 3D inv...
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03/25/2020
Convexification and experimental data for a 3D inverse scattering problem with the moving point source
Inverse scattering problems of the reconstructions of physical propertie...
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02/04/2020
Convexification for a 1D Hyperbolic Coefficient Inverse Problem with Single Measurement Data
A version of the convexification numerical method for a Coefficient Inve...
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11/11/2019