Probability theory and related fields, ISSN 1432-2064, 2018, Volume 173, Issue 3-4, pp. 1063 - 1098

...Probab. Theory Relat. Fields (2019) 173:1063–1098 https://doi.org/10.1007/s00440-018-0848-7 Regularization by noise for stochastic Hamilton–Jacobi equations...

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 2, pp. 719 - 732

.... This approximation process is also applied to the viscosity solutions of the discounted Hamilton–Jacobi equations.

Aubry–Mather theory | Weak KAM theory | Hamilton–Jacobi equations | Lasry–Lions regularization | MATHEMATICS | Hamilton-Jacobi equations | HILBERT-SPACES | SET | LAX-OLEINIK | LEMMA | POINT-OF-VIEW | DYNAMICS | Lasry-Lions regularization | Aubry-Mather theory | REGULARIZATION

Aubry–Mather theory | Weak KAM theory | Hamilton–Jacobi equations | Lasry–Lions regularization | MATHEMATICS | Hamilton-Jacobi equations | HILBERT-SPACES | SET | LAX-OLEINIK | LEMMA | POINT-OF-VIEW | DYNAMICS | Lasry-Lions regularization | Aubry-Mather theory | REGULARIZATION

Journal Article

SIAM journal on scientific computing, ISSN 1095-7197, 2018, Volume 40, Issue 2, pp. A629 - A652

...) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed...

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

Journal Article

ASYMPTOTIC ANALYSIS, ISSN 0921-7134, 2019, Volume 115, Issue 1-2, pp. 63 - 94

...) -> (t/epsilon, x/epsilon) of an age-structured equation describing the subdiffusive motion of, e.g., some protein inside a biological cell...

renewal equation | MATHEMATICS, APPLIED | WKB approximation | Hamilton-Jacobi equation | Age-structured PDE | CYTOPLASM | DYNAMICS | DIFFUSION | anomalous diffusion | MODEL | AGE | Constraining | Mathematics - Analysis of PDEs

renewal equation | MATHEMATICS, APPLIED | WKB approximation | Hamilton-Jacobi equation | Age-structured PDE | CYTOPLASM | DYNAMICS | DIFFUSION | anomalous diffusion | MODEL | AGE | Constraining | Mathematics - Analysis of PDEs

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2019, Volume 349, pp. 17 - 44

...) equations that has recently emerged in nonlinear solid mechanics. The solution W of the prototypical version of the HJ equations considered here corresponds physically...

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Journal Article

Nonlinear differential equations and applications, ISSN 1420-9004, 2012, Volume 20, Issue 3, pp. 413 - 445

...–Jacobi equations on the network and we study related comparison principles. Under suitable assumptions, we prove in particular that the value function is the unique constrained viscosity solution of the Hamilton...

Networks | Secondary 34H05 | 35F21 | Analysis | Optimal control | Graphs | Mathematics | Hamilton–Jacobi equations | Primary 35R02 | 35Q93 | 49J15 | Viscosity solutions | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | STATE CONSTRAINTS | BELLMAN EQUATIONS | Analysis of PDEs

Networks | Secondary 34H05 | 35F21 | Analysis | Optimal control | Graphs | Mathematics | Hamilton–Jacobi equations | Primary 35R02 | 35Q93 | 49J15 | Viscosity solutions | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | STATE CONSTRAINTS | BELLMAN EQUATIONS | Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2017, Volume 263, Issue 12, pp. 8418 - 8466

...–Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed...

Stratified structure | Hamilton–Jacobi equations | State constraint problems | Control problem on networks | MATHEMATICS | Hamilton-Jacobi equations | R-N | BELLMAN APPROACH | EIKONAL EQUATIONS | Analysis of PDEs | Mathematics | Optimization and Control

Stratified structure | Hamilton–Jacobi equations | State constraint problems | Control problem on networks | MATHEMATICS | Hamilton-Jacobi equations | R-N | BELLMAN APPROACH | EIKONAL EQUATIONS | Analysis of PDEs | Mathematics | Optimization and Control

Journal Article

2017, Probability theory and stochastic modelling, ISBN 9783319530666, Volume 82., xxiii, 916 pages

Providing an introduction to stochastic optimal control in inﬁnite dimension, this book gives a complete account of the theory of second-order HJB equations...

Hamiltonian systems | Hamilton-Jacobi equations | Stochastic processes | Hilbert space | Mathematical models | Stochastic models | Mathematical optimization | Probabilities | Functional analysis | Probability Theory and Stochastic Processes | Mathematics | Functional Analysis | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Partial Differential Equations | Stochastic control theory | Control theory | Geometry, Infinitesimal

Hamiltonian systems | Hamilton-Jacobi equations | Stochastic processes | Hilbert space | Mathematical models | Stochastic models | Mathematical optimization | Probabilities | Functional analysis | Probability Theory and Stochastic Processes | Mathematics | Functional Analysis | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Partial Differential Equations | Stochastic control theory | Control theory | Geometry, Infinitesimal

eBook

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 4/2013, Volume 110, Issue 14, pp. 5374 - 5379

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world...

Amplitude | Continuity equations | Hamilton Jacobi equation | Classical mechanics | Quantum mechanics | Wave equations | Particle mass | Matter waves | Mathematical constants | Coordinate systems | DERIVATION | ELECTRON | QUASI-CLASSICAL THEORY | MULTIDISCIPLINARY SCIENCES | WAVE MECHANICS | PRINCIPLE | QUANTUM-MECHANICS | EIGEN-VALUE-PROBLEM | Models, Theoretical | Mechanics | Quantum Theory | Time Factors | Hamilton-Jacobi equations | Schrodinger equation | Research | Statistical mechanics | Quantum theory | Physical Sciences

Amplitude | Continuity equations | Hamilton Jacobi equation | Classical mechanics | Quantum mechanics | Wave equations | Particle mass | Matter waves | Mathematical constants | Coordinate systems | DERIVATION | ELECTRON | QUASI-CLASSICAL THEORY | MULTIDISCIPLINARY SCIENCES | WAVE MECHANICS | PRINCIPLE | QUANTUM-MECHANICS | EIGEN-VALUE-PROBLEM | Models, Theoretical | Mechanics | Quantum Theory | Time Factors | Hamilton-Jacobi equations | Schrodinger equation | Research | Statistical mechanics | Quantum theory | Physical Sciences

Journal Article

Potential Analysis, ISSN 0926-2601, 2/2012, Volume 36, Issue 2, pp. 317 - 337

...Potential Anal (2012) 36:317–337 DOI 10.1007/s11118-011-9232-2 Functional Inequalities and Hamilton–Jacobi Equations in Geodesic Spaces Zoltán M. Balogh...

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Journal Article

Annals of Physics, ISSN 0003-4916, 10/2016, Volume 373, pp. 325 - 345

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation...

Damped harmonic oscillator | Dissipative quantum trajectory | Logarithmic nonlinear Schrödinger equation | Quantum Hamilton–Jacobi equation | Dissipative system | HIDDEN-VARIABLES | PHYSICS, MULTIDISCIPLINARY | Quantum Hamilton-Jacobi equation | Logarithmic nonlinear Schrodinger equation | SUGGESTED INTERPRETATION | MOTION | 2-DIMENSIONAL REACTIVE SCATTERING | WAVE-PACKET DYNAMICS | SYSTEMS | FIELD EQUATION | GROUND-STATE ENERGY | SCHRODINGER-LANGEVIN EQUATION | HYDRODYNAMIC EQUATIONS | Newton's laws of motion | Analysis | Partial differential equations | Quantum physics | Nonlinear equations | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | QUANTUM SYSTEMS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS OF MOTION | TRAJECTORIES | HAMILTON-JACOBI EQUATIONS | HARMONIC OSCILLATORS | WAVE FUNCTIONS

Damped harmonic oscillator | Dissipative quantum trajectory | Logarithmic nonlinear Schrödinger equation | Quantum Hamilton–Jacobi equation | Dissipative system | HIDDEN-VARIABLES | PHYSICS, MULTIDISCIPLINARY | Quantum Hamilton-Jacobi equation | Logarithmic nonlinear Schrodinger equation | SUGGESTED INTERPRETATION | MOTION | 2-DIMENSIONAL REACTIVE SCATTERING | WAVE-PACKET DYNAMICS | SYSTEMS | FIELD EQUATION | GROUND-STATE ENERGY | SCHRODINGER-LANGEVIN EQUATION | HYDRODYNAMIC EQUATIONS | Newton's laws of motion | Analysis | Partial differential equations | Quantum physics | Nonlinear equations | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | QUANTUM SYSTEMS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS OF MOTION | TRAJECTORIES | HAMILTON-JACOBI EQUATIONS | HARMONIC OSCILLATORS | WAVE FUNCTIONS

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2006, Volume 44, Issue 2, pp. 879 - 895

Convergent numerical schemes for degenerate elliptic partial differential equations are constructed and implemented...

Viscosity | Approximation | Mathematical monotonicity | Partial differential equations | Hamilton Jacobi equation | Elliptic equations | Boundary conditions | Mathematics | Mathematical functions | Coefficients | Monotone schemes | Free boundary problems | Finite difference schemes | Viscosity solution | Hamilton-Jabobi equation | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | free boundary problems | finite difference schemes | APPROXIMATIONS | STABILITY | NONOSCILLATORY SCHEMES | UNIQUENESS | viscosity solution | MOTION | MEAN-CURVATURE | partial differential equations | OPERATORS | monotone schemes

Viscosity | Approximation | Mathematical monotonicity | Partial differential equations | Hamilton Jacobi equation | Elliptic equations | Boundary conditions | Mathematics | Mathematical functions | Coefficients | Monotone schemes | Free boundary problems | Finite difference schemes | Viscosity solution | Hamilton-Jabobi equation | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | free boundary problems | finite difference schemes | APPROXIMATIONS | STABILITY | NONOSCILLATORY SCHEMES | UNIQUENESS | viscosity solution | MOTION | MEAN-CURVATURE | partial differential equations | OPERATORS | monotone schemes

Journal Article

2004, ISBN 0817640843, xii, 304

Book

Journal of Computational Physics, ISSN 0021-9991, 10/2016, Volume 322, pp. 199 - 223

...–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited...

Eikonal equation | Hamilton–Jacobi | Dynamic games | Parallel computing | Fast sweeping | Optimal control | FAST MARCHING METHOD | Hamilton-Jacobi | FAST ITERATIVE METHOD | ALGORITHMS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE CALCULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STEADY-STATE | CONSERVATION-LAWS | EIKONAL EQUATIONS | Computer science | Wave propagation | Algorithms | Multiprocessing | Analysis | Seismic waves | Mechanical engineering | Methods | EIKONAL APPROXIMATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | COMPUTER ARCHITECTURE | SEISMIC WAVES | WAVE PROPAGATION | HAMILTON-JACOBI EQUATIONS | OPTIMAL CONTROL

Eikonal equation | Hamilton–Jacobi | Dynamic games | Parallel computing | Fast sweeping | Optimal control | FAST MARCHING METHOD | Hamilton-Jacobi | FAST ITERATIVE METHOD | ALGORITHMS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE CALCULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STEADY-STATE | CONSERVATION-LAWS | EIKONAL EQUATIONS | Computer science | Wave propagation | Algorithms | Multiprocessing | Analysis | Seismic waves | Mechanical engineering | Methods | EIKONAL APPROXIMATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | COMPUTER ARCHITECTURE | SEISMIC WAVES | WAVE PROPAGATION | HAMILTON-JACOBI EQUATIONS | OPTIMAL CONTROL

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 1, pp. 345 - 364

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton Jacobi equations...

Nonlinear adjoint methods | nonconvex Hamilton–Jacobi equations | Discounted approximation | Ergodic problems | AUBRY-MATHER THEORY | VISCOSITY SOLUTIONS | discounted approximation | LAGRANGIAN SYSTEMS | nonconvex Hamilton-Jacobi equations | HOMOGENIZATION | PDE | MATHEMATICS | CONVEX HAMILTONIANS | ADJOINT | ergodic problems | CONVERGENCE | nonlinear adjoint methods

Nonlinear adjoint methods | nonconvex Hamilton–Jacobi equations | Discounted approximation | Ergodic problems | AUBRY-MATHER THEORY | VISCOSITY SOLUTIONS | discounted approximation | LAGRANGIAN SYSTEMS | nonconvex Hamilton-Jacobi equations | HOMOGENIZATION | PDE | MATHEMATICS | CONVEX HAMILTONIANS | ADJOINT | ergodic problems | CONVERGENCE | nonlinear adjoint methods

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 1/2018, Volume 74, Issue 1, pp. 145 - 174

...) partial differential equations. These nonsymmetric linear systems are uniformly bounded and coercive with respect to a related symmetric bilinear form, that is associated to a matrix $$\mathbf...

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Finite element methods | Hamilton–Jacobi–Bellman equations | 35J66 | Approximation in discontinuous spaces | Algorithms | 65F10 | GMRES | Mathematical and Computational Engineering | Preconditioners | Domain decomposition | 65N22 | 65N55 | 65N30 | MATHEMATICS, APPLIED | ALGORITHM | ADDITIVE SCHWARZ METHODS | Hamilton-Jacobi-Bellman equations | FINITE-ELEMENT APPROXIMATION | Analysis | Differential equations | Mathematics - Numerical Analysis | Numerical Analysis

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Finite element methods | Hamilton–Jacobi–Bellman equations | 35J66 | Approximation in discontinuous spaces | Algorithms | 65F10 | GMRES | Mathematical and Computational Engineering | Preconditioners | Domain decomposition | 65N22 | 65N55 | 65N30 | MATHEMATICS, APPLIED | ALGORITHM | ADDITIVE SCHWARZ METHODS | Hamilton-Jacobi-Bellman equations | FINITE-ELEMENT APPROXIMATION | Analysis | Differential equations | Mathematics - Numerical Analysis | Numerical Analysis

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 11/2017, Volume 108, Issue 5, pp. 751 - 782

We continue the study of the homogenization of coercive non-convex Hamilton–Jacobi equations in random media identifying two general classes of Hamiltonians with very distinct behavior...

Stochastic homogenization | Hamilton–Jacobi equations | Viscosity solutions | MATHEMATICS | Hamilton-Jacobi equations | MATHEMATICS, APPLIED

Stochastic homogenization | Hamilton–Jacobi equations | Viscosity solutions | MATHEMATICS | Hamilton-Jacobi equations | MATHEMATICS, APPLIED

Journal Article

1977, ISBN 0120893509, Volume 131., xi, 147

Book

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 1, pp. 137 - 162

We study the convergence of monotone P1 finite element methods on unstructured meshes for fully nonlinear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems...

Viscosity | Finite element method | Mathematical problems | Approximation | Mathematical monotonicity | Optimal control | Numerical methods | Mathematical functions | Numerical schemes | Partial differential equations | Finite element methods | Hamilton-Jacobi- Bellman equations | Viscosity solutions | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | finite element methods | Hamilton-Jacobi-Bellman equations | DIFFUSION | partial differential equations | viscosity solutions | DISCRETE MAXIMUM PRINCIPLE | DIFFERENCE APPROXIMATIONS | SCHEMES | Operators | Discretization | Mathematical analysis | Consistency | Projection | Diffusion | Convergence

Viscosity | Finite element method | Mathematical problems | Approximation | Mathematical monotonicity | Optimal control | Numerical methods | Mathematical functions | Numerical schemes | Partial differential equations | Finite element methods | Hamilton-Jacobi- Bellman equations | Viscosity solutions | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | finite element methods | Hamilton-Jacobi-Bellman equations | DIFFUSION | partial differential equations | viscosity solutions | DISCRETE MAXIMUM PRINCIPLE | DIFFERENCE APPROXIMATIONS | SCHEMES | Operators | Discretization | Mathematical analysis | Consistency | Projection | Diffusion | Convergence

Journal Article