International Journal of Imaging Systems and Technology, ISSN 0899-9457, 09/2019, Volume 29, Issue 3, pp. 195 - 209

At present, digital image processing plays a vital role in medical imaging areas and specifically in magnetic resonance imaging (MRI) of brain images such as...

adaptive Haar wavelet transform | non‐linear APDE | false‐hit | missed‐term | new convergent K‐means clustering | false-hit | missed-term | non-linear APDE | new convergent K-means clustering | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Magnetic resonance imaging | Image processing | Medical imaging equipment

adaptive Haar wavelet transform | non‐linear APDE | false‐hit | missed‐term | new convergent K‐means clustering | false-hit | missed-term | non-linear APDE | new convergent K-means clustering | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Magnetic resonance imaging | Image processing | Medical imaging equipment

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 03/2019, Volume 18, Issue 2, pp. 603 - 623

The initial value problem for some coupled non-linear wave equations is investigated. In the defocusing case, global well-posedness and ill-posedness results...

Instability | Global well-posedness | Non-linear Klein-Gordon system | Scattering | Blow-up | SYSTEM | MATHEMATICS, APPLIED | ENERGY | SOBOLEV SPACE | global well-posedness | CAUCHY-PROBLEM | 2D WAVE-EQUATION | EXPONENTIAL-GROWTH | MATHEMATICS | scattering | REGULARITY | blow-up | instability | GLOBAL-SOLUTIONS

Instability | Global well-posedness | Non-linear Klein-Gordon system | Scattering | Blow-up | SYSTEM | MATHEMATICS, APPLIED | ENERGY | SOBOLEV SPACE | global well-posedness | CAUCHY-PROBLEM | 2D WAVE-EQUATION | EXPONENTIAL-GROWTH | MATHEMATICS | scattering | REGULARITY | blow-up | instability | GLOBAL-SOLUTIONS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2019, Volume 39, Issue 5, pp. 2893 - 2913

We prove convergence of a variational formulation of the BDF2 method applied to the non-linear Fokker-Planck equation. Our approach is inspired by the...

Non-linear diffusion equations | BDF2 | Gradient flow | Minimizing movements | Second order scheme | MATHEMATICS, APPLIED | APPROXIMATION | CONTINUITY EQUATIONS | CROSS-DIFFUSION SYSTEMS | MATHEMATICS | SCHEME | DISCRETIZATION | second order scheme | DRIFT-DIFFUSION | CONVERGENCE | minimizing movements | NUMERICAL-SIMULATION | non-linear diffusion equations | AGGREGATION

Non-linear diffusion equations | BDF2 | Gradient flow | Minimizing movements | Second order scheme | MATHEMATICS, APPLIED | APPROXIMATION | CONTINUITY EQUATIONS | CROSS-DIFFUSION SYSTEMS | MATHEMATICS | SCHEME | DISCRETIZATION | second order scheme | DRIFT-DIFFUSION | CONVERGENCE | minimizing movements | NUMERICAL-SIMULATION | non-linear diffusion equations | AGGREGATION

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2016, Volume 6, Issue 4, pp. 955 - 976

Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time-dependent quantum Hamiltonians (H) over cap (t) when this...

Strichartz estimate | Herman-Kluk formula | Non-linear time-dependent Schrödinger equations | MATHEMATICS | MATHEMATICS, APPLIED | CONSTRUCTION | SCHRODINGER EVOLUTION-EQUATIONS | FORMULAS | Non-linear time-dependent Schrodinger equations | FUNDAMENTAL SOLUTION

Strichartz estimate | Herman-Kluk formula | Non-linear time-dependent Schrödinger equations | MATHEMATICS | MATHEMATICS, APPLIED | CONSTRUCTION | SCHRODINGER EVOLUTION-EQUATIONS | FORMULAS | Non-linear time-dependent Schrodinger equations | FUNDAMENTAL SOLUTION

Journal Article

NONLINEARITY, ISSN 0951-7715, 08/2017, Volume 30, Issue 8, pp. 3271 - 3303

We consider a nonlinear Schrodinger equation (NLS) posed on a graph (or network) composed of a generic compact part to which a finite number of half-lines are...

MATHEMATICS, APPLIED | quantum graphs | non-linear Schrodinger equation | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION

MATHEMATICS, APPLIED | quantum graphs | non-linear Schrodinger equation | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2019, Volume 39, Issue 4, pp. 1821 - 1889

This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the...

Convergence to equilibrium | Fokker-Planck equation | Gradient flow | Non-linear non-local PDE | Coarsening | Entropy method | MATHEMATICS, APPLIED | BEHAVIOR | coarsening | conver- gence to equilibrium | SOBOLEV INEQUALITIES | FAMILY | MATHEMATICS | SLYOZOV | Non-linear non-local pde | entropy method | EQUILIBRIUM | VERSION | DIFFUSION | gradient flow

Convergence to equilibrium | Fokker-Planck equation | Gradient flow | Non-linear non-local PDE | Coarsening | Entropy method | MATHEMATICS, APPLIED | BEHAVIOR | coarsening | conver- gence to equilibrium | SOBOLEV INEQUALITIES | FAMILY | MATHEMATICS | SLYOZOV | Non-linear non-local pde | entropy method | EQUILIBRIUM | VERSION | DIFFUSION | gradient flow

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2019, Volume 182, pp. 316 - 349

Let be a domain of , . The classical Caffarelli–Kohn–Nirenberg inequality rewrites as the following inequality: for any and any , there exists a constant such...

Hardy–Sobolev inequalities | Non linear elliptic critical equations | Non-smooth geometry | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONEXISTENCE | ELLIPTIC-EQUATIONS | Hardy-Sobolev inequalities | Geometry | Singularities | Curvature | Smooth boundaries

Hardy–Sobolev inequalities | Non linear elliptic critical equations | Non-smooth geometry | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONEXISTENCE | ELLIPTIC-EQUATIONS | Hardy-Sobolev inequalities | Geometry | Singularities | Curvature | Smooth boundaries

Journal Article

Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 24, pp. 1 - 28

This paper is concerned with the internal exact controllability of the following model of dynamical elasticity equations for incompressible materials with a...

Incompressible materials | Uniform decay rates | Non linear damping | Internal exact controllability | MATHEMATICS | non linear damping | MATHEMATICS, APPLIED | incompressible materials | COMPACT SURFACES | uniform decay rates | STABILIZATION | internal exact controllability | SEMILINEAR WAVE-EQUATION | ASYMPTOTIC STABILITY | ENERGY DECAY | DOMAINS

Incompressible materials | Uniform decay rates | Non linear damping | Internal exact controllability | MATHEMATICS | non linear damping | MATHEMATICS, APPLIED | incompressible materials | COMPACT SURFACES | uniform decay rates | STABILIZATION | internal exact controllability | SEMILINEAR WAVE-EQUATION | ASYMPTOTIC STABILITY | ENERGY DECAY | DOMAINS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 3, p. 35202

We investigate dispersive and Strichartz estimates for the Schrodinger time evolution propagator e(-itH) on a star-shaped metric graph. The linear operator, H,...

Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS

Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS

Journal Article

Inverse Problems, ISSN 0266-5611, 08/2018, Volume 34, Issue 10, p. 104004

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded...

acousto-electric tomography | hybrid imaging | non-linear conjugate gradient | non-linear PDE optimization | DENSITY | MATHEMATICS, APPLIED | INVERSE DIFFUSION | CONDUCTIVITY | RECONSTRUCTION | PHYSICS, MATHEMATICAL | Mathematics - Optimization and Control

acousto-electric tomography | hybrid imaging | non-linear conjugate gradient | non-linear PDE optimization | DENSITY | MATHEMATICS, APPLIED | INVERSE DIFFUSION | CONDUCTIVITY | RECONSTRUCTION | PHYSICS, MATHEMATICAL | Mathematics - Optimization and Control

Journal Article

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Unique determination of sound speeds for coupled systems of semi-linear wave equations

Indagationes Mathematicae, ISSN 0019-3577, 09/2019, Volume 30, Issue 5, pp. 904 - 919

We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval and a bounded domain in with boundary . We show...

Coupled systems | Inverse problems | Non-linear hyperbolic equations | To be checked by Faculty | MATHEMATICS | GLOBAL EXISTENCE | RECONSTRUCTION | RIEMANNIAN MANIFOLD | PROPAGATION

Coupled systems | Inverse problems | Non-linear hyperbolic equations | To be checked by Faculty | MATHEMATICS | GLOBAL EXISTENCE | RECONSTRUCTION | RIEMANNIAN MANIFOLD | PROPAGATION

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An application of the Nash–Moser theorem to the vacuum boundary problem of gaseous stars

Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 2, pp. 803 - 843

We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler–Poisson equations in the...

Nash–Moser theory | Vacuum boundary | Spherically symmetric solutions | Gaseous stars | Non-linear hyperbolic equations | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | PHYSICAL VACUUM | Nash-Moser theory | SPHERICALLY SYMMETRIC MOTIONS | WELL-POSEDNESS | Mathematics - Analysis of PDEs

Nash–Moser theory | Vacuum boundary | Spherically symmetric solutions | Gaseous stars | Non-linear hyperbolic equations | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | PHYSICAL VACUUM | Nash-Moser theory | SPHERICALLY SYMMETRIC MOTIONS | WELL-POSEDNESS | Mathematics - Analysis of PDEs

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 05/2017, Volume 42, Issue 5, pp. 731 - 756

We prove an adiabatic theorem for the nonautonomous semilinear Gross-Pitaevskii equation. More precisely, we assume that the external potential decays suitably...

non-autonomous dynamical systems | soliton | 82C10 | Adiabatic theory | 35Q55 | 81V70 | 35Q41 | non-linear Schrödinger equation | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | non-linear Schrodinger equation | MATHEMATICS | EVOLUTION | SOLITARY WAVES | RESONANCE | DYNAMICS | ASYMPTOTIC STABILITY | GROUND-STATES | SCATTERING | Adiabatic flow | Infinity | Decay | Conductivity | Ground state | Bifurcations | Helium

non-autonomous dynamical systems | soliton | 82C10 | Adiabatic theory | 35Q55 | 81V70 | 35Q41 | non-linear Schrödinger equation | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | non-linear Schrodinger equation | MATHEMATICS | EVOLUTION | SOLITARY WAVES | RESONANCE | DYNAMICS | ASYMPTOTIC STABILITY | GROUND-STATES | SCATTERING | Adiabatic flow | Infinity | Decay | Conductivity | Ground state | Bifurcations | Helium

Journal Article

Geophysical Journal International, ISSN 0956-540X, 10/2013, Volume 195, Issue 1, pp. 582 - 596

We propose a numerical algorithm for solving first arrival transmission traveltime tomography problems where the underlying slowness is piecewise continuous....

Non-linear differential equations | Tomography | Numerical solutions | TENSOR-FIELDS | VISCOSITY SOLUTIONS | X-RAY TRANSFORM | HAMILTON-JACOBI EQUATIONS | BOUNDARY RIGIDITY | GEOCHEMISTRY & GEOPHYSICS | FAST SWEEPING METHOD | APPROXIMATE INVERSES | INVERSE PROBLEMS | EIKONAL EQUATIONS | SCHEMES

Non-linear differential equations | Tomography | Numerical solutions | TENSOR-FIELDS | VISCOSITY SOLUTIONS | X-RAY TRANSFORM | HAMILTON-JACOBI EQUATIONS | BOUNDARY RIGIDITY | GEOCHEMISTRY & GEOPHYSICS | FAST SWEEPING METHOD | APPROXIMATE INVERSES | INVERSE PROBLEMS | EIKONAL EQUATIONS | SCHEMES

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Standing waves for the NLS on the double-bridge graph and a rational–irrational dichotomy

Journal of Differential Equations, ISSN 0022-0396, 01/2019, Volume 266, Issue 1, pp. 147 - 178

We study standing waves of NLS equation posed on the : two semi-infinite half-lines attached at a circle. At the two vertices Kirchhoff boundary conditions are...

Standing waves | Non-linear Schrödinger equation | Quantum graphs | MATHEMATICS | GROUND-STATE | EXPANSIONS | DEPENDENT BOUNDARY-CONDITIONS | NONLINEAR SCHRODINGER-EQUATION | Non-linear Schrodinger equation | ORBITAL STABILITY

Standing waves | Non-linear Schrödinger equation | Quantum graphs | MATHEMATICS | GROUND-STATE | EXPANSIONS | DEPENDENT BOUNDARY-CONDITIONS | NONLINEAR SCHRODINGER-EQUATION | Non-linear Schrodinger equation | ORBITAL STABILITY

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2018, Volume 51, Issue 40, p. 405201

We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose-Einstein condensate and then...

Spinor Bose-Einstein condensates | Many-body quantum dynamics | Cubic NLS | Mean-field | Effective non-linear evolution equations | Gross-Pitaevskii scaling | Reduced density matrix | Partial trace | mean-field and Gross-Pitaevskii scaling | DERIVATION | many-body quantum dynamics | PHYSICS, MULTIDISCIPLINARY | reduced density matrix | QUANTUM | spinor Bose-Einstein condensates | effective non-linear evolution equations | PHYSICS, MATHEMATICAL | cubic NLS | partial trace | GROSS-PITAEVSKII EQUATION

Spinor Bose-Einstein condensates | Many-body quantum dynamics | Cubic NLS | Mean-field | Effective non-linear evolution equations | Gross-Pitaevskii scaling | Reduced density matrix | Partial trace | mean-field and Gross-Pitaevskii scaling | DERIVATION | many-body quantum dynamics | PHYSICS, MULTIDISCIPLINARY | reduced density matrix | QUANTUM | spinor Bose-Einstein condensates | effective non-linear evolution equations | PHYSICS, MATHEMATICAL | cubic NLS | partial trace | GROSS-PITAEVSKII EQUATION

Journal Article

Journal of Hyperbolic Differential Equations, ISSN 0219-8916, 06/2018, Volume 15, Issue 2, pp. 219 - 258

We prove the non-linear stability of a system of non-linear wave equations satisfying the weak null condition. In particular, this includes the case of the...

Non-linear wave equation | Kaluza-klein spacetime | Einstein equations | VACUUM | MATHEMATICS, APPLIED | non-linear wave equation | GLOBAL STABILITY | MINKOWSKI SPACE | EQUATIONS | Kaluza-Klein spacetime | PHYSICS, MATHEMATICAL | RELATIVITY

Non-linear wave equation | Kaluza-klein spacetime | Einstein equations | VACUUM | MATHEMATICS, APPLIED | non-linear wave equation | GLOBAL STABILITY | MINKOWSKI SPACE | EQUATIONS | Kaluza-Klein spacetime | PHYSICS, MATHEMATICAL | RELATIVITY

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 04/2019, Volume 64, Issue 4, pp. 1403 - 1414

This paper concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the...

Stability | Estimation | Korteweg-de Vries non-linear equation | time delay | Delays | Mathematical model | Exponential stability | Observability | Dispersion | Lyapunov function | Lyapunov functional | time-delay | exponential stability | ROBUSTNESS | RESPECT | STABILITY | SYSTEMS | DE-VRIES EQUATION | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Observability (systems) | Liapunov functions | Decay rate | Computer simulation | Feedback | Time delay systems | Mathematics | Engineering Sciences | Analysis of PDEs | Automatic

Stability | Estimation | Korteweg-de Vries non-linear equation | time delay | Delays | Mathematical model | Exponential stability | Observability | Dispersion | Lyapunov function | Lyapunov functional | time-delay | exponential stability | ROBUSTNESS | RESPECT | STABILITY | SYSTEMS | DE-VRIES EQUATION | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Observability (systems) | Liapunov functions | Decay rate | Computer simulation | Feedback | Time delay systems | Mathematics | Engineering Sciences | Analysis of PDEs | Automatic

Journal Article

Nonlinearity, ISSN 0951-7715, 07/2017, Volume 30, Issue 8, pp. 3271 - 3303

We consider a nonlinear Schrodinger equation (NLS) posed on a graph (or network) composed of a generic compact part to which a finite number of half-lines are...

non-linear Schrodinger equation | concentrationcompactness techniques | quantum graphs | MATHEMATICS, APPLIED | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION

non-linear Schrodinger equation | concentrationcompactness techniques | quantum graphs | MATHEMATICS, APPLIED | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION

Journal Article

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Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator

Analysis and PDE, ISSN 2157-5045, 2014, Volume 7, Issue 4, pp. 997 - 102

Thanks to an approach inspired by Burq and Lebeau [Ann. Sci. Ec. Norm. Super. (4) 6:6 (2013)], we prove stochastic versions of Strichartz estimates for...

Global solutions | Random initial conditions | Scattering | Supercritical nonlinear Schrödinger equation | Harmonic oscillator | supercritical nonlinear Schrodinger equation | EXISTENCE | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | harmonic oscillator | POTENTIALS | MATHEMATICS | INVARIANT-MEASURES | scattering | global solutions | OPERATOR | DATA CAUCHY-THEORY | random initial conditions

Global solutions | Random initial conditions | Scattering | Supercritical nonlinear Schrödinger equation | Harmonic oscillator | supercritical nonlinear Schrodinger equation | EXISTENCE | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | harmonic oscillator | POTENTIALS | MATHEMATICS | INVARIANT-MEASURES | scattering | global solutions | OPERATOR | DATA CAUCHY-THEORY | random initial conditions

Journal Article

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