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Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2017, Volume 108, Issue 6, pp. 818 - 840
We prove the existence of nontrivial global minimizers of the Allen–Cahn equation in dimension 8 and above. More precisely, given any strict area-minimizing... 
Minimal cones | De Giorgi conjecture | Global minimizer | Allen–Cahn equation | MATHEMATICS, APPLIED | CONES | STABILITY | 1D SYMMETRY | CONJECTURE | BISTABLE DIFFUSION-EQUATIONS | MATHEMATICS | SADDLE-SHAPED SOLUTIONS | REGULARITY | Allen-Cahn equation | ELLIPTIC-EQUATIONS | MINIMAL HYPERSURFACES | SURFACES
Journal Article
Geophysical Research Letters, ISSN 0094-8276, 03/2015, Volume 42, Issue 5, pp. 1312 - 1317
Through polarization and spectra analysis of the magnetic field observed by the Van Allen Probe A, we present two typical cases of O+ band electromagnetic ion... 
EMIC waves | O+ ion torus | oxygen band | Van Allen Probes | SATELLITE | INSTABILITY | O plus ion torus | ION-CYCLOTRON WAVES | MAGNETOSPHERE | PLASMAPAUSE | STORMS | PLASMASPHERIC PLUME | GEOSCIENCES, MULTIDISCIPLINARY | AKEBONO | FREQUENCY | GENERATION | Bands | Polarization | Geomagnetism | Toruses | Spectra | Plasmasphere | Magnetic fields | Waves | Cyclotrons
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2019, Volume 231, Issue 2, pp. 1129 - 1216
Journal Article
Journal of Geophysical Research: Space Physics, ISSN 2169-9380, 06/2015, Volume 120, Issue 6, pp. 4400 - 4408
Journal Article
by Qi, RS and Wang, XJ
JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 08/2019, Volume 80, Issue 2, pp. 1171 - 1194
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn... 
Additive noise | Strong approximation | Finite element method | MATHEMATICS, APPLIED | Stochastic Allen-Cahn equation | DISCRETIZATION | APPROXIMATION | DIFFERENTIAL-EQUATIONS | TIME | Backward Euler scheme | STRONG-CONVERGENCE | Analysis | Methods
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 10/2018, Volume 76, Issue 8, pp. 1876 - 1892
We study (time) fractional Allen–Cahn and Cahn–Hilliard phase-field models to account for the anomalously subdiffusive transport behavior in heterogeneous... 
Scaling law | Tunable decay behavior | Time fractional Cahn–Hilliard model | Sensitivity analysis | Time fractional Allen–Cahn model | FLUIDS | MATHEMATICS, APPLIED | APPROXIMATION | DIFFERENCE SCHEME | Time fractional Allen-Cahn model | ENERGY STABLE SCHEME | DYNAMICS | DIFFUSION | Time fractional Cahn-Hilliard model | EQUATION
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2019, Volume 35, Issue 3, pp. 1290 - 1300
In this paper, a new numerical method is proposed and analyzed for the Allen–Cahn (AC) equation. We divide the AC equation into linear section and nonlinear... 
adaptive algorithm | finite element method | SCR | operator splitting | Allen–Cahn equation | MATHEMATICS, APPLIED | Allen-Cahn equation | Finite element method | Algorithms | Analysis | Methods | Splitting | Mathematical analysis | Numerical methods | Adaptive algorithms | Finite element analysis | Nonlinear programming
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 4/2019, Volume 79, Issue 1, pp. 593 - 623
Journal Article