Conditions for boundary feedback stabilizability of non-uniform linear 2 × 2 hyperbolic systems over a bounded interval are investigated. Themain result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered interval. This result is used to give explicit conditions for the existence of stabilizing...

In this paper, we consider the problems of stability analysis and control synthesis for first-order hyperbolic linear Partial Differential Equations (PDEs) over a bounded interval with spatially varying coefficients. We propose Linear Matrix Inequalities (LMI) conditions for the stability and for the design of boundary and distributed control for the system. These conditions involve an infinite...

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves stationary steady states (lake at rest) and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these fe...

In this paper we prove the Poincaré lemma on some n-dimensional corank 1 sub-Riemannian structures, formulating the (n−1)n(n +3n−2) 8 necessarily and sufficiently ’curl-vanishing’ compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. Our proof is based on a Poincaré lemma stated on Riemannian manifolds and a suitable Cesàro-Volterra...

Abstract. We are interested in simulating overland flow on agricultural fields during rainfall events. In this context, we definitely have to cope with dry/wet interfaces and water inflow on dry soil. The model considered is the Shallow Water system (or Saint-Venant equations) without infiltration. Moreover, the model has to be completed with friction terms. It is numerically solved by a finite...

We consider the Saint-Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic stead...

RI~SUMt~ Par une mdthode applicable ~t un tr~s grand nombre de milieu anisotropique, l'auteur utilise les in6galit6s concern~nt la d~croissance de l'6nergie darts le cas d'un probl~me plan et dans l'hypoth6se de conditions 61astostatiques lin~ahes, l'auteur pr6cise la validit6 du principe de Saint-Venant dans le cadre de ses applications. Une limite in fdrieure (en fonction des constantes 61ast...

We are interested in simulating overland flow on agricultural fields during rainfall events. The model considered is the shallow water system (or Saint-Venant equations) without infiltration, complemented with a friction term. In this context, we definitely have to cope with dry/wet interfaces and water inflow on dry soil. We present a simplified one-dimensional model, discretized with a well-b...