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