Abstract
The mathematical properties of a nonlinear parabolic equation arising in the modelling of concentrated suspension flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact, a linear advection equation). Depending on the initial data, at least two situations can be encountered: the equation may have a unique solution in a convenient class, or it may have infinitely many solutions. The present article is the theoretical side of a joint project with rheologists, aiming at better understanding the flows of complex fluids.
| Original language | English |
|---|---|
| Pages (from-to) | 60-82 |
| Number of pages | 23 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 37 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Dec 2005 |
Keywords
- Complex fluids
- Concentrated suspensions
- Degenerate parabolic equation
- Non-Newtonian flows
- Nonlinear parabolic equation
- Viscosity solutions
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