Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Tao, Terence (2005)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “On phase segregation in nonlocal two-particle Hartree systems”
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes
Christian Heinemann, Christiane Kraus (2014)
Mathematica Bohemica
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This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a...
Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
Jürg Fröhlich, Enno Lenzmann (2003-2004)
Séminaire Équations aux dérivées partielles
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We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle...
On a Cahn–Hilliard model for phase separation with elastic misfit
Harald Garcke (2005)
Annales de l'I.H.P. Analyse non linéaire
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Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates
Amandine Aftalion, Xavier Blanc (2008)
Annales de l'I.H.P. Analyse non linéaire
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Analysis of a force-based quasicontinuum approximation
Matthew Dobson, Mitchell Luskin (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation can be derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical “ghost” forces that occur in the atomistic to continuum interface during constant strain. The algorithmic simplicity and consistency with the purely atomistic...