Publications

 Ray Abney, Thuy T. Le, Loc H. Nguyen, and Cam Peters, A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data, preprint arXiv:2309.14599, 2023.

 Thuy T. Le, Linh V. Nguyen, Loc H. Nguyen, and Hyunha Park, The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients, to appear in Computers and Mathematics with Applications, preprint arXiv:2308.13152, 2024.

 Huynh P. N. Le, Thuy T. Le, Loc H. Nguyen, The Carleman convexification method for Hamilton-Jacobi equations on the whole space, to appear in Computers and Mathematics with Applications, preprint arXiv:2206.09824, 2024.

 Anuj Abhishek, Thuy T. Le, Loc H. Nguyen, Taufiquar Khan, The Carleman- Newton method to globally reconstruct a source term for nonlinear parabolic equation, to appear in Journal of Computational and Applied Mathematics, 2024. (link)

 Dinh-Nho Hào, Thuy T. Le and Loc H. Nguyen, The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data, to appear in Communications in Nonlinear Science and Numerical Simulation, preprint arXiv:2305.19528, 2023.

 Phuong M. Nguyen, Thuy T. Le, Loc H. Nguyen, and Michael V. Klibanov, Numerical differentiation by the polynomial-exponential basis, to appear in Journal of Applied and Industrial Mathematics, preprint arXiv:2304.05909, 2023.

 Thuy T. Le, Vo A. Khoa, Michael V. Klibanov, Loc H. Nguyen, Grant Bidney, and Vasily Astratov, Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data, to appear in Journal of Applied and Industrial Mathematics, preprint arXiv:2306.00761, 2023.

 Thuy T. Le, Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method. In D-L Nguyen, L. H. Nguyen, and T-P. Nguyen, editors, Advances in Inverse problems for Partial Differential Equations, volume 784, pages 145-167, Contemporary Mathematics, American Mathematical Society, 2023. 

 T. T. Le, L. H. Nguyen, and H. V. Tran, A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications, Computers and Mathematics with Applications, Volume 125, Pages 13-24, 2022.

 T.T. Le and L. H. Nguyen, The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem, Journal of Scientific Computing 91:74, 2022.

 M Hashemitaheri, TT Le, H Cherukuri, T Khan, A Multivariate Newton-Raphson Method Approach to Extract Structural Dynamics Parameters During Milling Operations, AeroMat Conference and Exposition: AeroMat 2022 - Pasadena Convention Center, Pasadena, CA, USA, 2022.

 Thuy T. Le, Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, and Lam Nguyen, Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data, Inverse Problems 38, 045002, 2022.

 M. V. Klibanov, T. T. Le, L. H. Nguyen, A. Sullivan, and L. Nguyen, Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data, Inverse Problems and Imaging, 16, p. 1579-1618, 2022. 

 Thuy T. Le and Loc H. Nguyen,  A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data,  Journal of Ill-posed and Inverse Problems 30, p 256-286, 2022.

 T. T. Le, L. H. Nguyen, T-P. Nguyen and W. Powell, The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations, Journal of Scientific Computing 87:90, 2021. (link) 

 Michael V. Klibanov,  Thuy T. Le,  and Loc H. Nguyen, Convergent numerical method for a linearized travel time tomography problem with incomplete data, SIAM Journal on Scientific Computing 42(2020) B1173-B1192, 2020. (link)