Consider a viscous scalar conservation law with smooth, possibly non-convex flux. Assume that the (arbitrarily large) initial data remains in a small neighbourhood of given states u−, u+ as x → ± ∞, with u−, u+ connected by a stable shock profile. We then show that the solution eventually forms a viscous shock. The time needed for the shock to appear is the main focus of the present analysis.
|Original language||English (US)|
|Number of pages||11|
|Journal||International Journal of Dynamical Systems and Differential Equations|
|State||Published - Jan 1 2007|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Control and Optimization