Walter H. Aschbacher
We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.
Submitted September 26, 2008. Published January 12, 2009.
Math Subject Classifications: 35Q40, 35Q35, 35J60, 65M60, 65N30.
Key Words: Hartree equation; quantum many-body system; weakly nonlinear dispersive waves; Newtonian gravity; Galerkin theory; finite element methods; discretization accuracy.
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| Walter H. Aschbacher |
Technische Universität München
Zentrum Mathematik, M5
85747 Garching, Germany
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