Inverse problems, ISSN 1361-6420, 2007, Volume 23, Issue 3, pp. 987 - 1010

There exists a vast literature on convergence rates results for Tikhonov regularized minimizers. We are concerned with the solution of nonlinear ill-posed...

MATHEMATICS, APPLIED | ILL-POSEDNESS | INVERSE PROBLEM | PHYSICS, MATHEMATICAL | VOLATILITY

MATHEMATICS, APPLIED | ILL-POSEDNESS | INVERSE PROBLEM | PHYSICS, MATHEMATICAL | VOLATILITY

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 02/2016, Volume 105, Issue 8, pp. 620 - 640

Summary This paper proposes a new method called time‐domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems....

ill‐posedness | time‐domain Galerkin method | shape function approximation | dynamic load identification | regularization | Dynamic load identification | Time-domain galerkin method | Regularization | Ill-posedness | Shape function approximation | ILL-POSED PROBLEMS | ITERATIVE REGULARIZATION | RECONSTRUCTION | ill-posedness | FORCE IDENTIFICATION | BRIDGE | LEAST-SQUARES | time-domain Galerkin method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | REGULARIZATION METHOD | INVERSE PROBLEMS | STRUCTURAL DYNAMICS | Approximation | Kernel functions | Mathematical analysis | Mathematical models | Dynamic loads | Weighting functions | Shape functions | Galerkin methods

ill‐posedness | time‐domain Galerkin method | shape function approximation | dynamic load identification | regularization | Dynamic load identification | Time-domain galerkin method | Regularization | Ill-posedness | Shape function approximation | ILL-POSED PROBLEMS | ITERATIVE REGULARIZATION | RECONSTRUCTION | ill-posedness | FORCE IDENTIFICATION | BRIDGE | LEAST-SQUARES | time-domain Galerkin method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | REGULARIZATION METHOD | INVERSE PROBLEMS | STRUCTURAL DYNAMICS | Approximation | Kernel functions | Mathematical analysis | Mathematical models | Dynamic loads | Weighting functions | Shape functions | Galerkin methods

Journal Article

Annales Scientifiques de l'Ecole Normale Superieure, ISSN 0012-9593, 11/2015, Volume 48, Issue 6, pp. 1273 - 1325

It has been thought for a while that the Prandtl system is only well-posed under the Oleinik monotonicity assumption or under an analyticity assumption. We...

EXISTENCE | MATHEMATICS | REGULARITY | STABILITY | ILL-POSEDNESS | EULER | EQUATION

EXISTENCE | MATHEMATICS | REGULARITY | STABILITY | ILL-POSEDNESS | EULER | EQUATION

Journal Article

Econometrica, ISSN 0012-9682, 7/2017, Volume 85, Issue 4, pp. 1303 - 1320

The ill-posedness of the nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper,...

NOTES AND COMMENTS | Nonparametric estimation | monotonicity | measure of ill‐posedness | instrumental variable | measure of ill-posedness | KERNEL REGRESSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SHAPE RESTRICTIONS | REGRESSION FUNCTION | CONSTRAINTS | STATISTICS & PROBABILITY | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Studies | Economic models | Instrumental variable estimation | Simulation | Regularity | Estimators

NOTES AND COMMENTS | Nonparametric estimation | monotonicity | measure of ill‐posedness | instrumental variable | measure of ill-posedness | KERNEL REGRESSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SHAPE RESTRICTIONS | REGRESSION FUNCTION | CONSTRAINTS | STATISTICS & PROBABILITY | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Studies | Economic models | Instrumental variable estimation | Simulation | Regularity | Estimators

Journal Article

Inverse problems, ISSN 1361-6420, 2005, Volume 21, Issue 3, pp. 1027 - 1045

This paper investigates the stable identification of local volatility surfaces sigma (S, t) in the Black-Scholes/Dupire equation from market prices of European...

MATHEMATICS, APPLIED | ILL-POSEDNESS | PHYSICS, MATHEMATICAL | VOLATILITY

MATHEMATICS, APPLIED | ILL-POSEDNESS | PHYSICS, MATHEMATICAL | VOLATILITY

Journal Article

Communications on pure and applied mathematics, ISSN 0010-3640, 2015, Volume 68, Issue 10, pp. 1683 - 1741

We prove local existence and uniqueness for the two‐dimensional Prandtl system in weighted Sobolev spaces under Oleinik's monotonicity assumption. In...

BOUNDARY-LAYER EQUATIONS | ANALYTIC SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | VANISHING VISCOSITY | WELL-POSEDNESS | HALF-SPACE | ZERO VISCOSITY LIMIT | ILL-POSEDNESS | EULER | INVISCID LIMIT

BOUNDARY-LAYER EQUATIONS | ANALYTIC SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | VANISHING VISCOSITY | WELL-POSEDNESS | HALF-SPACE | ZERO VISCOSITY LIMIT | ILL-POSEDNESS | EULER | INVISCID LIMIT

Journal Article

Nonlinearity, ISSN 0951-7715, 02/2012, Volume 25, Issue 2, pp. 449 - 479

This work studies the initial value problem for a Camassa-Holm type equation with cubic nonlinearities that has been recently discovered by Vladimir Novikov to...

PEAKON | MATHEMATICS, APPLIED | NONUNIFORM DEPENDENCE | WELL-POSEDNESS | ILL-POSEDNESS | PHYSICS, MATHEMATICAL | INTEGRABLE EQUATION | Work study | Approximation | Fluid dynamics | Mathematical analysis | Nonlinearity | Initial value problems | Galerkin methods | Optimization

PEAKON | MATHEMATICS, APPLIED | NONUNIFORM DEPENDENCE | WELL-POSEDNESS | ILL-POSEDNESS | PHYSICS, MATHEMATICAL | INTEGRABLE EQUATION | Work study | Approximation | Fluid dynamics | Mathematical analysis | Nonlinearity | Initial value problems | Galerkin methods | Optimization

Journal Article

Mechanical systems and signal processing, ISSN 0888-3270, 2017, Volume 95, pp. 273 - 285

•A new method for dynamic load identification is proposed.•Dynamic load in each time element is approximated by shape function.•Accuracy is improved and the...

Load identification | Time element | Ill-posedness | Interpolation function | Singular value decomposition | REGULARIZATION METHOD | FORCE IDENTIFICATION | ENGINEERING, MECHANICAL

Load identification | Time element | Ill-posedness | Interpolation function | Singular value decomposition | REGULARIZATION METHOD | FORCE IDENTIFICATION | ENGINEERING, MECHANICAL

Journal Article

Structural control and health monitoring, ISSN 1545-2255, 2018, Volume 25, Issue 12, pp. e2255 - n/a

This paper presents a novel sparse‐regularized minimum constitutive relation error (min‐CRE) approach for structural damage identification with modal data. In...

ill‐posedness | sparse regularization | incomplete modal data | constitutive relation error (CRE) | damage identification | ill-posedness | ENGINEERING, CIVIL | INSTRUMENTS & INSTRUMENTATION | CONSTRUCTION & BUILDING TECHNOLOGY | CANTILEVER BEAM | FREQUENCY | FIELD MEASUREMENT | Constitutive relationships | Sensitivity analysis | Computer simulation | Identification | Optimization | Modal data | Errors | Inverse problems | Damage detection | Computer applications | Structural damage | Robustness | Objective function | Nonlinear programming | Regularization

ill‐posedness | sparse regularization | incomplete modal data | constitutive relation error (CRE) | damage identification | ill-posedness | ENGINEERING, CIVIL | INSTRUMENTS & INSTRUMENTATION | CONSTRUCTION & BUILDING TECHNOLOGY | CANTILEVER BEAM | FREQUENCY | FIELD MEASUREMENT | Constitutive relationships | Sensitivity analysis | Computer simulation | Identification | Optimization | Modal data | Errors | Inverse problems | Damage detection | Computer applications | Structural damage | Robustness | Objective function | Nonlinear programming | Regularization

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 03/2016, Volume 472, Issue 2187, p. 20150808

Electrified liquids are well known to be prone to a variety of interfacial instabilities that result in the onset of apparent interfacial singularities and...

Screening | Coulomb fission | Free boundary | Geometric variational problem | Ill-posedness | screening | free boundary | ELECTROSPRAY | INSTABILITY | RAYLEIGH LIMIT | BEHAVIOR | MULTIDISCIPLINARY SCIENCES | geometric variational problem | ill-posedness | LEVITATED MICRODROPLETS | DROPLETS | STABILITY LIMIT | DYNAMICS | FISSION | ISOPERIMETRIC PROBLEM | 1008 | 120

Screening | Coulomb fission | Free boundary | Geometric variational problem | Ill-posedness | screening | free boundary | ELECTROSPRAY | INSTABILITY | RAYLEIGH LIMIT | BEHAVIOR | MULTIDISCIPLINARY SCIENCES | geometric variational problem | ill-posedness | LEVITATED MICRODROPLETS | DROPLETS | STABILITY LIMIT | DYNAMICS | FISSION | ISOPERIMETRIC PROBLEM | 1008 | 120

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2018, Volume 370, Issue 7, pp. 4709 - 4730

We construct an example showing that the solution map of the Euler equations is not continuous in the Holder space from C-1,C-alpha to L-t(infinity)...

Hölder spaces | Solution map | Euler equations | FLUIDS | MATHEMATICS | INSTABILITY | HYDRODYNAMICS | DYNAMICS | ILL-POSEDNESS | solution map | LOCAL EXISTENCE | Holder spaces

Hölder spaces | Solution map | Euler equations | FLUIDS | MATHEMATICS | INSTABILITY | HYDRODYNAMICS | DYNAMICS | ILL-POSEDNESS | solution map | LOCAL EXISTENCE | Holder spaces

Journal Article

Geometric and functional analysis, ISSN 1420-8970, 2018, Volume 28, Issue 4, pp. 1062 - 1090

We present a general method for obtaining conservation laws for integrable PDE at negative regularity and exhibit its application to KdV, NLS, and mKdV. Our...

Analysis | Mathematics | MATHEMATICS | SOLITON-SOLUTIONS | DE-VRIES EQUATION | ILL-POSEDNESS | KDV | GLOBAL WELL-POSEDNESS | Environmental law

Analysis | Mathematics | MATHEMATICS | SOLITON-SOLUTIONS | DE-VRIES EQUATION | ILL-POSEDNESS | KDV | GLOBAL WELL-POSEDNESS | Environmental law

Journal Article

International Journal of Engineering Science, ISSN 0020-7225, 11/2014, Volume 84, pp. 147 - 155

This paper re-examines the boundary conditions at the moving front of a hydraulic fracture when the fluid front has coalesced with the crack edge. This...

Speed equation | Hydraulic fractures | Ill-posedness | PLANE-STRAIN PROPAGATION | ENGINEERING, MULTIDISCIPLINARY | TIP REGION | FLUID-DRIVEN FRACTURE | ASYMPTOTICS | CRACK | SIMULATION | Fluids | Fracture mechanics | Fluid dynamics | Hydraulics | Asymptotic properties | Fluid flow | Apertures | Boundary conditions

Speed equation | Hydraulic fractures | Ill-posedness | PLANE-STRAIN PROPAGATION | ENGINEERING, MULTIDISCIPLINARY | TIP REGION | FLUID-DRIVEN FRACTURE | ASYMPTOTICS | CRACK | SIMULATION | Fluids | Fracture mechanics | Fluid dynamics | Hydraulics | Asymptotic properties | Fluid flow | Apertures | Boundary conditions

Journal Article

International Journal of Circuit Theory and Applications, ISSN 0098-9886, 12/2017, Volume 45, Issue 12, pp. 1920 - 1941

Summary In this paper, we evaluate a useful general model for linear direct current (DC) networks, containing design parameters, multiple inputs and outputs....

ill‐posedness | general multi input‐output description | practical experiments | multivariate polynomials | General multi input-output description | Multivariate polynomials | Ill-posedness | Practical experiments | general multi input-output description | ILL-POSED PROBLEMS | ill-posedness | SYMBOLIC NETWORK FUNCTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DC to DC | Design parameters | Electric converters | Computer simulation | Circuits | Direct current | Rational functions | Linear equations | Linear functions

ill‐posedness | general multi input‐output description | practical experiments | multivariate polynomials | General multi input-output description | Multivariate polynomials | Ill-posedness | Practical experiments | general multi input-output description | ILL-POSED PROBLEMS | ill-posedness | SYMBOLIC NETWORK FUNCTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DC to DC | Design parameters | Electric converters | Computer simulation | Circuits | Direct current | Rational functions | Linear equations | Linear functions

Journal Article

15.
Full Text
Ill-posedness of the Cauchy problem for the Chern–Simons–Dirac system in one dimension

Journal of Differential Equations, ISSN 0022-0396, 02/2015, Volume 258, Issue 4, pp. 1356 - 1394

We consider the Cauchy problem for the Chern–Simons–Dirac system in one spatial dimension. For this problem, Bournaveas, Candy, and Machihara (2012) proved the...

Chern–Simons–Dirac system | Ill-posedness | Cauchy problem | Well-posedness | Chern-Simons-Dirac system

Chern–Simons–Dirac system | Ill-posedness | Cauchy problem | Well-posedness | Chern-Simons-Dirac system

Journal Article

Advances in physics, ISSN 1460-6976, 2006, Volume 55, Issue 3-4, pp. 279 - 348

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail...

PHYSICS, CONDENSED MATTER | CONTACT | VISCOELASTIC PROPERTIES | RATE-DEPENDENT FRICTION | PHASE-TRANSITIONS | DYNAMICS | RUBBER-FRICTION | ILL-POSEDNESS | SURFACE-ROUGHNESS | STATIC FRICTION | PHYSICAL ANALYSIS | Condensed Matter | Physics

PHYSICS, CONDENSED MATTER | CONTACT | VISCOELASTIC PROPERTIES | RATE-DEPENDENT FRICTION | PHASE-TRANSITIONS | DYNAMICS | RUBBER-FRICTION | ILL-POSEDNESS | SURFACE-ROUGHNESS | STATIC FRICTION | PHYSICAL ANALYSIS | Condensed Matter | Physics

Journal Article

Nonlinearity, ISSN 1361-6544, 2019, Volume 32, Issue 8, pp. 2914 - 2954

We study the well-posedness of the initial value problem for fully nonlinear evolution equations, u(t) + f [u] = 0, where f may depend on up to the first three...

gauged energy method | MATHEMATICS, APPLIED | well-posedness | REGULARITY | anti-diffusion | CAUCHY-PROBLEM | ILL-POSEDNESS | dispersive | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs

gauged energy method | MATHEMATICS, APPLIED | well-posedness | REGULARITY | anti-diffusion | CAUCHY-PROBLEM | ILL-POSEDNESS | dispersive | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs

Journal Article

18.
Full Text
On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2017, Volume 38, pp. 35 - 48

Persistence of spatial analyticity is studied for periodic solutions of the dispersion-generalized KdV equation ut−|Dx|αux+uux=0 for α≥2. For a class of...

Gevrey regularity | KdV equation | Radius of analyticity | Algebraic decrease | Bourgain spaces | MATHEMATICS, APPLIED | WELL-POSEDNESS | ILL-POSEDNESS | PROJECTION | NAVIER-STOKES EQUATIONS | RADIUS | CONVERGENCE | KLEIN-GORDON EQUATIONS

Gevrey regularity | KdV equation | Radius of analyticity | Algebraic decrease | Bourgain spaces | MATHEMATICS, APPLIED | WELL-POSEDNESS | ILL-POSEDNESS | PROJECTION | NAVIER-STOKES EQUATIONS | RADIUS | CONVERGENCE | KLEIN-GORDON EQUATIONS

Journal Article

Differential and Integral Equations, ISSN 0893-4983, 03/2009, Volume 22, Issue 3-4, pp. 201 - 224

For s > 1 two sequences of CH solutions living in a bounded subset of the Sobolev space H-s(R) are constructed, whose distance at the initial time is...

MATHEMATICS | MATHEMATICS, APPLIED | WELL-POSEDNESS | ILL-POSEDNESS | SHALLOW-WATER EQUATION | CAMASSA-HOLM EQUATION

MATHEMATICS | MATHEMATICS, APPLIED | WELL-POSEDNESS | ILL-POSEDNESS | SHALLOW-WATER EQUATION | CAMASSA-HOLM EQUATION

Journal Article

European journal of operational research, ISSN 0377-2217, 2019, Volume 275, Issue 2, pp. 755 - 767

•Study of optimal investment strategies maximizing the Omega ratio.•Maximizing the Omega ratio may lead to excessive risk taking (ill-posed problem).•Bounded...

Investment analysis | Omega ratio | Optimal portfolio choice | Performance measurement | Ill-posedness | PORTFOLIO PERFORMANCE EVALUATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNCERTAINTY | GAIN | DEPENDENCE | Usage | Investors | Ratio analysis | Management

Investment analysis | Omega ratio | Optimal portfolio choice | Performance measurement | Ill-posedness | PORTFOLIO PERFORMANCE EVALUATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNCERTAINTY | GAIN | DEPENDENCE | Usage | Investors | Ratio analysis | Management

Journal Article