We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real...

We address the issue of the exponential stability (in L2-norm) of the classical solutions of the linearised Saint-Venant equations for a sloping channel. We give an explicit sufficient dissipative condition which guarantees the exponential stability under subcritical flow conditions without additional assumptions on the size of the bottom and friction slopes. The stability analysis relies on th...

We present the Lie symmetry analysis for a hyperbolic partial differential system known as one-dimensional Saint-Venant-Exner model. The model describes shallow-water systems with bed evolution given by Exner terms. sediment flux is considered to be power-law function of velocity fluid. admitted symmetries are classified according power index flux. Furthermore, optimal determined in all cases. ...