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Abstract: In this Note, we prove a Carleman''s estimate for the integro-differential hyperbolic system of the viscoelasticity problem and we use this estimate to obtain a stability result for the inverse problem of recovering a viscoelastic coefficient from a unique internal measure. To cite this article: M. de Buhan, A. Osses, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]

Abstract: We present a Cosserat-based 3D–1D dimensional reduction for the viscoelastic finite strain model introduced by P. Neff. The reduced 1D model preserves observer invariance. We prove the existence and uniqueness of the solution of the reduced coupled minimization/evolution problem. To cite this article: J. Beyrouthy, C. R. Acad. Sci. Paris, Ser. I 345 (2007). [Copyright &y& Elsevier]

This paper is concerned with incompressible viscoelastic fluids which obey a differential constitutive law of White–Metzner type. We establish the existence and uniqueness of local solutions in 3-D as well as the global existence of small solutions. We then deduce the existence and asymptotic stability of small periodic and stationary solutions. Finally, we prove that the 2-D results obtained in Hakim (J. Math. Anal. Appl. 185 (1994) 675–705) remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity (Navier–Stokes equation) and the transport equation verified by the extra-stress tensor. To cite this article: L. Molinet, R. Talhouk, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]

Let α be a positive number. The one-dimensional viscoelastic problem utt−uxx−αuxxt=f, x∈(−∞,0], t∈[0,+∞), with unilateral boundary conditions u(0,·)⩾0, (ux+αuxt)(0,·)⩾0, (u(ux+αuxt))(0,·)=0, can be reduced to the following variational inequality: λ1*w=g+b, w⩾0, b⩾0, 〈w,b〉=0. Here λˆ1(ω) is the causal determination of iω√ of 1+iαω. We show that the energy losses are purely viscous; this result is a consequence of the relation 〈w˙,b〉=0; since a priori, b is a measure and w˙ is defined only almost everywhere, this relation is not trivial. To cite this article: A. Petrov, M. Schatzman, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 983–988. [Copyright &y& Elsevier]