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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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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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05/21/2022
Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method
We propose a global convergent numerical method to reconstruct the initi...
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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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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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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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11/11/2019