Abstract
A diffuse interface model for the one-phase Hele-Shaw problem is derived from a gradient flow characterization due to Otto (1998 Arch. Rat. Mech. Anal. 141 63). The resulting dynamical model yields a generalized form of Darcy's law, and reduces to a degenerate version of the well-known Cahn-Hilliard equation. Formal asymptotics illustrate the connection to the classical Hele-Shaw free boundary problem. Some example computations are carried out to demonstrate the flexibility of the modelling framework.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 49-66 |
| Number of pages | 18 |
| Journal | Nonlinearity |
| Volume | 16 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2003 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
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