Carleman estimate for the Schrödinger equation and application to magnetic inverse problems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.01.035 ◽

2019 ◽

Vol 474 (1) ◽

pp. 116-142 ◽

Author(s):

Xinchi Huang ◽

Yavar Kian ◽

Éric Soccorsi ◽

Masahiro Yamamoto

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Carleman Estimate

Download Full-text

Solving forward and inverse problems of the nonlinear Schrödinger equation with generalized PT-symmetric Scarf-II potential via the PINNs deep learning

Communications in Theoretical Physics ◽

10.1088/1572-9494/ac2055 ◽

2021 ◽

Author(s):

Jiaheng Li ◽

Biao Li

Keyword(s):

Deep Learning ◽

Inverse Problems ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

Download Full-text

Connection Between Time- and Frequency-Domain Three-Dimensional Inverse Problems for the Schrödinger Equation

Review of Progress in Quantitative Nondestructive Evaluation ◽

10.1007/978-1-4615-9421-5_60 ◽

1985 ◽

pp. 535-541

Author(s):

James H. Rose ◽

Margaret Cheney ◽

Brian DeFacio

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Frequency Domain ◽

Schrodinger Equation ◽

Three Dimensional

Download Full-text

Carleman inequalities and inverse problems for the Schrödinger equation

Comptes Rendus Mathematique ◽

10.1016/j.crma.2007.11.014 ◽

2008 ◽

Vol 346 (1-2) ◽

pp. 53-58 ◽

Author(s):

Alberto Mercado ◽

Axel Osses ◽

Lionel Rosier

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Carleman Inequalities

Download Full-text

A Hölder stability estimate for inverse problems for the ultrahyperbolic Schrödinger equation

Analysis and Mathematical Physics ◽

10.1007/s13324-019-00326-6 ◽

2019 ◽

Vol 9 (4) ◽

pp. 2171-2199 ◽

Author(s):

Fikret Gölgeleyen ◽

Özlem Kaytmaz

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Stability Estimate ◽

Hölder Stability

Download Full-text

Bernstein–von Mises theorems for statistical inverse problems I: Schrödinger equation

Journal of the European Mathematical Society ◽

10.4171/jems/975 ◽

2020 ◽

Vol 22 (8) ◽

pp. 2697-2750

Author(s):

Richard Nickl

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Statistical Inverse Problems ◽

Download Full-text

Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights

Inverse Problems ◽

10.1088/0266-5611/24/1/015017 ◽

2008 ◽

Vol 24 (1) ◽

pp. 015017 ◽

Author(s):

Alberto Mercado ◽

Axel Osses ◽

Lionel Rosier

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Carleman Inequalities

Download Full-text

The Darboux and Abraham-Moses transformations of the one-dimensional periodic Schrodinger equation and inverse problems

Inverse Problems ◽

10.1088/0266-5611/5/6/019 ◽

1989 ◽

Vol 5 (6) ◽

pp. 1145-1155 ◽

Author(s):

L Trlifaj

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

One Dimensional ◽

Download Full-text

Inverse problems in the coupling constant for the Schrodinger equation

Inverse Problems ◽

10.1088/0266-5611/5/3/004 ◽

1989 ◽

Vol 5 (3) ◽

pp. 257-268 ◽

Author(s):

K Chadan ◽

M Musette

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Coupling Constant

Download Full-text

On the application of continual integrals to the solution of certain inverse problems for the three-dimensional Schrodinger equation

Inverse Problems ◽

10.1088/0266-5611/7/1/009 ◽

1991 ◽

Vol 7 (1) ◽

pp. 85-100

Author(s):

G N Gestrin

Keyword(s):

Inverse Problems ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Three Dimensional

Download Full-text

Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with PT-symmetric harmonic potential via deep learning

Physics Letters A ◽

10.1016/j.physleta.2020.127010 ◽

2021 ◽

Vol 387 ◽

pp. 127010

Author(s):

Zijian Zhou ◽

Zhenya Yan

Keyword(s):

Deep Learning ◽

Inverse Problems ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Harmonic Potential ◽

Nonlinear Schrödinger

Download Full-text