Displaying similar documents to “A problem in Rayleigh-Taylor instability”

Guided waves in a fluid layer on an elastic irregular bottom.

Andrés Fraguela Collar (1996)

Publicacions Matemàtiques

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In this paper one considers the linearized problem to determine the movement of an ideal heavy fluid contained in an unbounded container withelastic walls. As initial data one knows the movement of both the bottom and the free surface of the fluid and also the strength of certain perturbation, strong enough to take the bottom out of its rest state. One important point to be considered regards the influence of the bottom’s geometry on the propagation of superficial waves....

Sensors and boundary state reconstruction of hyperbolic systems

El Hassan Zerrik, Hamid Bourray, Samir Ben Hadid (2010)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained...

Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients

Bruno Fornet (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface { x d = 0 } . Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is 𝔻 t + a ( x ) 𝔻 x , with s i g n ( x a ( x ) ) > 0 (expansive case not included in our first result), thus resulting in an infinity of weak solutions. Proving that this problem is uniformly Evans-stable, we...