We study the existence and the uniqueness of a positive connection, that is a stationary solution connecting the boundary data, for the initial-boundary value problem for the viscous shallow water system (Equation presented) in a bounded interval (-l, l) of the real line. We firstly consider the general case where the term of pressure P(u) satisfies P(0) = 0, P(+∞) = +∞, P'(u) and P"(u) > 0 ∀u < 0, and then we show properties of the steady state in the relevant case P(u) = κuγ, γ > 1. The viscous Saint-Venant system, corresponding to γ = 2, fits in the general framework.
EXISTENCE AND UNIQUENESS OF A POSITIVE CONNECTION FOR THE SCALAR VISCOUS SHALLOW WATER SYSTEM IN A BOUNDED INTERVAL
Strani M
2014-01-01
Abstract
We study the existence and the uniqueness of a positive connection, that is a stationary solution connecting the boundary data, for the initial-boundary value problem for the viscous shallow water system (Equation presented) in a bounded interval (-l, l) of the real line. We firstly consider the general case where the term of pressure P(u) satisfies P(0) = 0, P(+∞) = +∞, P'(u) and P"(u) > 0 ∀u < 0, and then we show properties of the steady state in the relevant case P(u) = κuγ, γ > 1. The viscous Saint-Venant system, corresponding to γ = 2, fits in the general framework.File in questo prodotto:
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