论文信息 - The viscous Cahn-Hilliard equation

The viscous Cahn-Hilliard equation

The viscous Cahn-Hilliard equation arises as a singular limit of the phase-field model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. The equation is in gradient form and possesses a compact global atUactor 4 comprising heteroclinic orbits between equilibria. Two classes of wmputati0n.m described,. First heteroclinic o&its on the global attractor are computed; by using the viscous Cahn-Hilliard equation to perform a homotopy. these results show that the orbits, md hence the geometry of the atmctors, are remarkably insensitive to whether the Allen-Cahn or Cahn-Hilliard equation is studied. Second, initial-value computations are described; these computations emphasize three differing mechanisms by which interfaces in the equation propagate for the case of very small penalization of interfacial energy Furthermore, convergence to an appropriate free boundary problem is demonstrated numerically. AMS classification scheme numbers: 35K35, 65N25, 65N35.65M99

C. M. Elliott | C M Elliott | M Six | M. Six

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