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Mathematics › Mathematical Physics

Advanced Mathematical Physics Problems

Works Count: 39346

Description

This cluster of papers focuses on the global well-posedness, scattering, and blow-up phenomena for various nonlinear wave equations, including the nonlinear Schrödinger equation, wave maps equation, Korteweg-de Vries equation, and dispersive equations. The research also explores the behavior of solitons and critical exponent for energy-critical equations.

Keywords

Global Well-Posedness; Nonlinear Schrödinger Equation; Scattering; Blow-Up; Dispersive Equations; Strichartz Estimates; Energy-Critical Equations; Wave Maps Equation; Korteweg-de Vries Equation; Solitons

Most Cited Works

Action Title Date Authors
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Nonlinear Dispersive Equations 2006-06-08 Terence Tao
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The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. 1984-04-01 Pierre‐Louis Lions
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Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities 2002-01-01 Élliott H. Lieb
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StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions 1984-12-01 Tosio Kato
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Remarks on the breakdown of smooth solutions for the 3-D Euler equations 1984-03-01 J. Thomas Beale T. Kato Andrew J. Majda
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Nonlinear-Evolution Equations of Physical Significance 1973-07-09 Mark J. Ablowitz D. J. Kaup Alan C. Newell Harvey Segur
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Orbital stability of standing waves for some nonlinear Schr�dinger equations 1982-12-01 Thierry Cazenave Pierre‐Louis Lions
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Model equations for long waves in nonlinear dispersive systems 1972-03-30 T. Brooke Benjamin Jerry L. Bona J. J. Mahony
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Stability theory of solitary waves in the presence of symmetry, II 1990-12-01 Manoussos G. Grillakis Jalal Shatah Walter A. Strauss
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Hitchhikerʼs guide to the fractional Sobolev spaces 2011-12-30 Eleonora Di Nezza Giampiero Palatucci Enrico Valdinoci
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Partial regularity of suitable weak solutions of the navier‐stokes equations 1982-11-01 Luis Caffarelli Robert V. Kohn Louis Nirenberg
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Subelliptic estimates and function spaces on nilpotent Lie groups 1975-12-01 Gerald B. Folland
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Nonlinear Schr�dinger equations and sharp interpolation estimates 1983-12-01 Michael I. Weinstein
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C1 + α local regularity of weak solutions of degenerate elliptic equations 1983-01-01 Emmanuele DiBenedetto
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An integrable shallow water equation with peaked solitons 1993-09-13 Roberto Camassa Darryl D. Holm
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Solutions in the large for nonlinear hyperbolic systems of equations 1965-11-01 James Glimm
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Weak solutions of nonlinear hyperbolic equations and their numerical computation 1954-02-01 Peter D. Lax
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Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group 1974-07-01 Gerald B. Folland E. M. Stein
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Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary 1992-09-01 Claude Bardos Gilles Lebeau Jeffrey Rauch
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Existence of solitary waves in higher dimensions 1977-06-01 Walter A. Strauss
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Universality and scaling in gravitational collapse of a massless scalar field 1993-01-04 Matthew W. Choptuik
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A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation 1993-03-01 Percy Deift Xin Zhou
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Ordinary differential equations, transport theory and Sobolev spaces 1989-10-01 Ronald J. DiPerna Pierre Louis Lions
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Nonlinear scalar field equations, I existence of a ground state 1983-12-01 Henri Berestycki P. L. Lions
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Global and local behavior of positive solutions of nonlinear elliptic equations 1981-07-01 Basilis Gidas Joel Spruck
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A connection between nonlinear evolution equations and ordinary differential equations of P-type. I 1980-04-01 Mark J. Ablowitz A. Ramani Harvey Segur
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Extensions of Hardy spaces and their use in analysis 1977-01-01 Ronald R. Coifman Guido Weiss
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Wave breaking for nonlinear nonlocal shallow water equations 1998-01-01 Adrian Constantin Joachim Escher
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Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations 2001-10-01 Liu Shi-Kuo Zuntao Fu Shida Liu Qiang Zhao
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A discrete transform and decompositions of distribution spaces 1990-10-01 Michael Frazier Björn Jawerth
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Integrals of nonlinear equations of evolution and solitary waves 1968-09-01 Peter D. Lax
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Endpoint Strichartz estimates 1998-10-01 M. Keel Terence Tao
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Solitary wave solutions for variant Boussinesq equations 1995-03-01 Ming L. Wang
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The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations 2008-05-29 Adrian Constantin David Lannes
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Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle 1993-04-01 Carlos E. Kenig Gustavo Ponce Luis Vega
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On the interior regularity of weak solutions of the Navier-Stokes equations 1962-01-01 James Serrin
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Operator expansion for high-energy scattering 1996-03-01 Ian Balitsky
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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations 1993-05-01 Jean Bourgain
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On a class of nonlinear Schr�dinger equations 1992-03-01 Paul H. Rabinowitz
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Singular integral equations 1954-06-01 Howard H. Brown
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Harmonic Analysis (PMS-43) 1993-12-31 Elias M. Stein
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Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems 2018-07-11 Flore K. Kunst Elisabet Edvardsson Jan Carl Budich Emil J. Bergholtz
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The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 1984-08-01 Pierre‐Louis Lions
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Quantum sine-Gordon equation as the massive Thirring model 1994-12-01 Sidney Coleman
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Review of AdS/CFT Integrability: An Overview 2011-10-26 Niklas Beisert Changrim Ahn Luis F. Alday Zoltán Bajnok J. M. Drummond Lisa Freyhult Nikolay Gromov Romuald A. Janik Vladimir Kazakov Thomas Klose
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Superconformal field theory on threebranes at a Calabi-Yau singularity 1998-12-01 Igor R. Klebanov Edward Witten
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Stability theory of solitary waves in the presence of symmetry, I 1987-09-01 Manoussos G. Grillakis Jalal Shatah Walter A. Strauss
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Time dependent boundary conditions for hyperbolic systems 1987-01-01 Kevin W. Thompson
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Dynamics of Viscous Compressible Fluids 2003-12-04 Eduard Feireisl
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Semilinear Schrödinger Equations 2003-09-16 Thierry Cazenave

Most Recent Works

Action Title Date Authors
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Breather, rational and semi-rational solutions of the generalized nonlocal Davey-Stewartson-type system 2025-05-02 Jiaqi Wang Zhonglong Zhao Yindi Liu
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Global well-posedness for 2D generalized parabolic Anderson model via paracontrolled calculus 2025-05-03 Hao Shen Rongchan Zhu Xiangchan Zhu
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Euler equations in Sobolev conormal spaces 2025-05-03 Mustafa Sencer Aydın Igor Kukavica
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On the exact traveling wave solutions to the Akbota-Gudekli-Kairat-Zhaidary equation and its numerical solutions 2025-05-03 Reda Ibrahim Ahmet Bekir Emad H. M. Zahran
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Modulational instability, bifurcation study, sensitivity analysis, and Jacobi elliptic waves of a resonant nonlinear Schrödinger equation 2025-05-04 K. Hosseini Farzaneh Alizadeh S. Kheybari Sekson Sirisubtawee M.S. Osman
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Rank-Two Reflexive Sheaves on the Projective Space with Second Chern Class Equal to Four 2025-05-04 Marcos Jardim Alan Muniz
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Inverse coefficient problem for wave equation with the generalized Riemann–Liouville time-derivative 2025-05-04 D. K. Durdiev H. H. Turdiev
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The Cauchy problem for semi-linear Klein-Gordon equations in Friedmann-Lemaître-Robertson-Walker spacetimes 2025-05-05 Makoto Nakamura Takuma Yoshizumi
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Evaluation of solutions of one class of finite-dimensional nonlinear equations. II 2025-05-05 B. D. Koshanov М. Отелбаев Abduhali Shynybekov
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Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations 2025-05-05 Yohei Fujishima Toru Kan
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The well-posedness of the stochastic nonlinear Schrödinger equations in $H^2(R^d)$ 2025-05-05 Isamu Dôku Shunya Hashimoto Shuji Machihara
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Multi-bump solutions for the double phase critical Schrödinger equations involving logarithmic nonlinearity 2025-05-05 Lifeng Guo Sihua Liang Bin Lin Patrizia Pucci
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Ground state solutions for the nonlinear problem involving exponential form of Born-Infeld-like 2025-05-05 Bingbing Dai Ruifeng Zhang
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Mass-critical focusing inhomogeneous NLS with inverse square potential 2025-05-05 Salah Boulaaras Tarek Saanouni
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On bound states of Schrödinger equation with vanishing magnetic potential 2025-05-05 Baihong Li Yuanhong Wei
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Semiclassical solutions for critical Schrödinger–Poisson systems involving multiple competing potentials 2025-05-04 Lingzheng Kong Haibo Chen
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Boundary Exponential Stabilization for the Linear KP-II Equation without Critical Size Restrictions 2025-05-05 Fernando A. Gallego Juan Ricardo Muñoz
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Propagation and interaction of local waves for a generalized Yu-Toda-Sasa-Fukuyama equation in fluids 2025-05-06 Xiao-Hong Yu Da-Wei Zuo
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Derivation and Multisoliton Solutions of the High‐Order Fractional Nonlinear SchröDinger Equation for the Rossby Waves 2025-05-06 Yi Liu Huanhe Dong Baojun Zhao Jingjing Li Xiaofeng Han
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Periodic focusing properties of circular Butterfly Vortex beams in the fractional Schrödinger equation with parabolic potential 2025-05-06 Yan Wang Zhirui Wang Ruifang Zhang
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Regular black holes from thin-shell collapse 2025-05-06 Pablo Bueno Pablo A. Cano Robie A. Hennigar Ángel Murcia
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Some remarks on a dispersal integral operator 2025-05-06 Francisco Júlio S. A. Corrêa Natan de Assis Lima
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Monotonicity of Limit Wave Speed in the pgKdV Equation with Nonlinear Terms of Arbitrarily High Degrees 2025-05-06 Ting An Yanfei Dai
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On the regularity of axially-symmetric solutions to the incompressible Navier-Stokes equations in a cylinder 2025-05-06 Wojciech S. Ożański Wojciech M. Zajączkowski
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Stability analysis for Kawahara equation with boundary time-varying delay 2025-05-07 Toufik Ennouari Abdellaziz Binid Ahmat Mahamat Taboye
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Complex exact solutions of the coupled higher-order nonlinear Schrödinger model with variable coefficients 2025-05-07 Yating Hao Yang Liu
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Fission and Fusion Solitons, and Some Interaction Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili-Yu-Toda-Sasa-Fukuyama Equation 2025-05-07 Junxia Li Zhimin Ma Han Hongwei Kong Yunhui Youhua Wei
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New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System 2025-05-07 Feriel Boudersa Abdelaziz Mennouni Ravi P. Agarwal
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Thermodynamics of Classical One-dimensional Generalized Nonlinear Klein-Gordon Lattice Model 2025-05-07 H. M. Jia Ning-Hua Tong
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Smooth dynamics of a sup-cubic wave equation with delays 2025-05-07 Hong-Fang Li Jia Qi Feng Zhou Kaixuan Zhu Xin Li
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Global well-posedness for the generalized derivative nonlinear Schrödinger equation 2025-05-07 Ben Pineau Mitchell A. Taylor
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Novel Breather, Lump and Interaction Solutions for (2+1)-dimensional Generalized Korteweg-De Vries Equation 2025-05-07 Nauman Raza Saima Arshed M. Irshad M. Higazy Y. S. Hamed
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Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted <i>L</i> <sup>∞</sup> spaces 2025-05-07 Ioakeim Ampatzoglou Joseph K. Miller Nataša Pavlović Maja Tasković
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Global refined Fujita-Kato solution of 3-D inhomogeneous incompressible Navier-Stokes equations with large density 2025-05-07 Hammadi Abidi Guilong Gui Ping Zhang
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Homogeneous solutions to the Einstein-matter equations with a magnetic field and a conformal gauge singularity 2025-05-07 Ho Lee Ernesto Nungesser John Stalker Paul Tod
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Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity 2025-05-06 Qingqing Peng Yikan Liu
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Global Classical Solutions to the Two-phase Flow Model with Slip Boundary Condition in 3D Bounded Domains 2025-05-05 Zilai Li Linlin Zhao
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Long-Time Behavior of an Arc-Shaped Vortex Filament and Its Application to the Stability of a Circular Vortex Filament 2025-05-08 Masashi Aiki
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Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in $$\mathbb {R}^3$$ 2025-05-08 Jeaheang Bang Zhuolun Yang
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The local limit of the quasilocal mass and mean quasilocal pressure on rigid spheres and rigid quasilocal frames in a general space-time 2025-05-08 Y.K. Foo Malcolm Anderson
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Rogue wave dynamics and energy spectra for the generalized Heisenberg spin chain equation 2025-05-08 Xue-Ke Liu Zhen Wang R. Du Xiao‐Yong Wen
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Dynamics of the Drinfeld-Sokolov-Wilson system: Well-posedness and (in)stability of the traveling waves 2025-05-09 Ognyan Christov Sevdzhan Hakkaev Seungly Oh Atanas Stefanov
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Semilinear wave equations with scale invariant structural damping and variable external forces 2025-05-09 Masao Yamazaki Taeko Yamazaki
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Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories 2025-05-09 Harold Blas
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Analytical solutions for the forced KdV equation with variable coefficients 2025-05-09 Ji Wang Jia Fu Jialin Dai
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Dynamical characteristics and modulation instability (MI) analysis of sharp ‎slope bell soliton and kink wave solutions to the perturbed space-time fractional Boussinesq equation 2025-05-08 Foyjonnesa Jobayad Bhuiyan Mst. Ummey Kulsum
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Formation of solitary wave solutions to nonlinear (3+1)-dimensional Boussinesq equation via analytical techniques 2025-05-09 Saima Arshed Ghazala Akram Maasoomah Sadaf Muhammad Sulaiman Riaz
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Global well-posedness for two-dimensional inhomogeneous viscous flows with rough data via dynamic interpolation 2025-05-10 Raphaël Danchin
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Observability of the Schrödinger equation with subquadratic confining potential in the Euclidean space 2025-05-10 Antoine Prouff
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Approximate controllability of a non-local hyperbolic coupled system 2025-05-10 Carole Louis-Rose