We study the existence of a positive connection, i.e. a stationary solution connecting the boundary data, for the initial-boundary value problem for the viscous shallow water system in a bounded interval (-a"", a"") of the real line. Subsequently, we investigate the asymptotic behavior of the time-dependent solutions, showing that they first develop into a layered function and then they drift towards the steady state in an exponentially long time interval. The main tool of our analysis is given by the derivation of an ODE for the interface location.
Long time dynamics of layered solutions to the shallow water equations
Strani M
2016-01-01
Abstract
We study the existence of a positive connection, i.e. a stationary solution connecting the boundary data, for the initial-boundary value problem for the viscous shallow water system in a bounded interval (-a"", a"") of the real line. Subsequently, we investigate the asymptotic behavior of the time-dependent solutions, showing that they first develop into a layered function and then they drift towards the steady state in an exponentially long time interval. The main tool of our analysis is given by the derivation of an ODE for the interface location.
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