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Communications on Pure and Applied Mathematics, ISSN 0010-3640, 02/2019, Volume 72, Issue 2, pp. 229 - 274
Journal Article
International Journal of Engineering Science, ISSN 0020-7225, 2006, Volume 44, Issue 11, pp. 730 - 737
The simultaneous effects of normal transpiration through and tangential movement of a semi-infinite plate on self-similar boundary layer flow beneath a uniform... 
Nonuniqueness | Transpiration | Similarity solutions | Stability | transpiration | WALL | similarity solutions | nonuniqueness | ENGINEERING, MULTIDISCIPLINARY | REVERSE FLOW | stability | Mechanical engineering | Analysis
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 6/2019, Volume 29, Issue 3, pp. 766 - 810
We prove that Bernoulli bond percolation on any nonamenable, Gromov hyperbolic, quasi-transitive graph has a phase in which there are infinitely many infinite... 
Analysis | Mathematics | MATHEMATICS | NONUNIQUENESS | SHARPNESS | PHASE-TRANSITION
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2015, Volume 281, pp. 845 - 856
In this paper we show by example that there is no uniform estimate for the Lp-Minkowski problem. As a result we obtain the nonuniqueness of solutions to the... 
Nonuniqueness | Monge–Ampère equation | Minkowski problem
Journal Article
Geophysics, ISSN 0016-8033, 2012, Volume 77, Issue 1, pp. W1 - W15
We analyze, through linear algebra, the topography of the cost functional in linear and nonlinear inverse problems with the aim of illuminating general... 
Inversion | Optimization | GEOCHEMISTRY & GEOPHYSICS | PRIOR INFORMATION | NONUNIQUENESS | MODELS | UNCERTAINTY | INACCURATE | ALGORITHMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2017, Volume 450, Issue 2, pp. 872 - 887
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability... 
Helmholtz equation | Stability | Inverse source problem | Stochastic differential equation | MATHEMATICS | NONUNIQUENESS | MATHEMATICS, APPLIED
Journal Article
Animal Behaviour, ISSN 0003-3472, 11/2013, Volume 86, Issue 5, pp. 1097 - 1105
To find a dominance order most consistent with a linear hierarchy, the I&SI method minimizes two criteria: first the number of inconsistencies I (i.e. number... 
matrix reordering technique | nonuniqueness | dominance ranking | inconsistent dyad | I&SI method | DomiCalc | Dominance ranking | Nonuniqueness | Inconsistent dyad | Matrix reordering technique | SOCIAL RANK | ZOOLOGY | APPROPRIATE ORDER | BEHAVIORAL SCIENCES | INDEX | MODEL
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 05/2019, Volume 91, pp. 106 - 112
We consider non-adiabatic combustion waves arising from a two-step exothermic system. Our previous work showed that in certain parameter regions, the... 
Travelling waves | Critical initial conditions | Bistability | NONUNIQUENESS | MATHEMATICS, APPLIED | REDUCTION | COMBUSTION WAVES | FLAME | SHS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2020, Volume 268, Issue 5, pp. 1873 - 1910
In this paper we give some Fujita type results for strongly p-coercive quasilinear parabolic differential inequalities with both a diffusion term and a... 
Global solutions | Nonexistence of solutions | Parabolic inequalities | MATHEMATICS | NONUNIQUENESS | NONEXISTENCE | GLOBAL EXISTENCE | DECAY | HEAT-EQUATION | CAUCHY-PROBLEM | BLOWUP
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 08/2018, Volume 265, Issue 4, pp. 1467 - 1487
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy,... 
EXISTENCE | MATHEMATICS | NONUNIQUENESS | INCOMPRESSIBLE EULER | STABILITY | WEAK-STRONG UNIQUENESS | EQUATIONS | SYSTEMS | RIEMANN SOLUTIONS
Journal Article
Geophysics, ISSN 0016-8033, 2006, Volume 71, Issue 6, pp. R131 - R138
We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach... 
Seismic waves | Inverse problems | TOMOGRAPHY | GEOCHEMISTRY & GEOPHYSICS | NONUNIQUENESS | RESOLUTION
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2005, Volume 60, Issue 3, pp. 515 - 545
We study the localization properties of weak solutions to the Dirichlet problem for the degenerate parabolic equation u t - div ( | u | γ ( x , t ) ∇ u ) = f ,... 
Nonlinear parabolic equations | Nonstandard growth conditions | MATHEMATICS | nonlinear parabolic equations | NONUNIQUENESS | MATHEMATICS, APPLIED | nonstandard growth conditions | SINGULARITIES
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/1995, Volume 12, Issue 2, pp. 173 - 200
We study the existence of infinitely many solutions for the Cauchy problem associated with the nonlinear heat equation ut = (um − 1ux)x in the fast diffusion... 
nonuniqueness | Bäcklund transform | Nonlinear heat equation | fast diffusion | 35 K 65 | 35 K 55
Journal Article
Journal of Hydrology, ISSN 0022-1694, 01/2019, Volume 568, pp. 416 - 426
•The rainfall Areal Reduction Factor (ARF) was investigated using radar rainfall.•The ARF decreases with increasing area while increases with... 
Rainfall | Spatial variability | Areal reduction factor | Radar | TRANSFORMATION | DERIVATION | NONUNIQUENESS | REFLECTIVITY | CATCHMENT | WATER RESOURCES | IDENTIFICATION | POINT RAINFALL | ENGINEERING, CIVIL | GEOSCIENCES, MULTIDISCIPLINARY | FREQUENCY | SCALE
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 04/2019, Volume 266, Issue 9, pp. 5971 - 5997
In this paper we establish various existence, nonexistence and multiplicity results for fully nonlinear Dirichlet problems associated to nonlocal... 
Fully nonlinear equations | Eigenvalue problem | Resonance phenomena | Integro-differential operators | MATHEMATICS | VISCOSITY SOLUTIONS | NONUNIQUENESS | EIGENVALUES | MAXIMUM PRINCIPLE | REGULARITY | ELLIPTIC-OPERATORS
Journal Article
Inverse Problems, ISSN 0266-5611, 06/2006, Volume 22, Issue 3, pp. 1023 - 1035
The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does... 
NONUNIQUENESS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | MAGNETOENCEPHALOGRAPHY
Journal Article
SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2018, Volume 78, Issue 5, pp. 2626 - 2647
We consider the radiative transfer equation (RTE) with two scalings in this paper: one is the diffusive scaling whose macroscopic limit is a diffusion... 
Transport equation | Stability | Fokker-Planck limit | Diffusion limit | Inverse problem | inverse problem | NONUNIQUENESS | MATHEMATICS, APPLIED | OPTICAL TOMOGRAPHY | transport equation | diffusion limit | stability | SCATTERING
Journal Article
NONLINEARITY, ISSN 0951-7715, 01/2020, Volume 33, Issue 1, pp. 139 - 155
We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill-posed... 
EXISTENCE | NONUNIQUENESS | DISSIPATION | MATHEMATICS, APPLIED | magnetohydrodynamic system | compressible flow | convex integration | CLASSICAL-SOLUTIONS | weak solutions | MHD EQUATIONS | PHYSICS, MATHEMATICAL | FLOW
Journal Article
Medical Physics, ISSN 0094-2405, 09/2017, Volume 44, Issue 9, pp. e202 - e206
Purpose The goal is to determine whether dual‐energy computed tomography (CT) leads to a unique reconstruction using two basis materials. Methods The... 
dual‐energy CT | proof by example | nonuniqueness | dual-energy CT | TOMOGRAPHY | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING
Journal Article
Inverse Problems, ISSN 0266-5611, 02/2018, Volume 34, Issue 2, p. 25004
We consider the inverse problem of reconstructing the optical parameters for the stationary radiative transfer equation (RTE) from velocity-averaged... 
diffusion approximation | radiative transfer | asymptotic limit | stability | NONUNIQUENESS | MATHEMATICS, APPLIED | OPTICAL TOMOGRAPHY | PHYSICS, MATHEMATICAL | Mathematics - Numerical Analysis
Journal Article
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