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Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer

Victor Péron (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions...

Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved L q -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...

Étude de l’équation 1 2 Δ u - u μ = 0 où μ est une mesure positive

Denis Feyel, A. de La Pradelle (1988)

Annales de l'institut Fourier

On montre que les solutions faibles de l’équation Δ u - u μ = 0 , où μ est une mesure positive négligeant les polaires, vérifient une inégalité de Harnack. On s’occupe également des sursolutions dont on fait la représentation intégrale a l’aide d’une fonction de Green. Comme les solutions sont discontinues, on est amené à utiliser les formules probabilistes.

Exact controllability of a pluridimensional coupled problem.

Serge Nicaise (1992)

Revista Matemática de la Universidad Complutense de Madrid

We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with...

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