In this work we study the existence, uniqueness and decay of solutions to a class of viscoelastic equations in a separable Hilbert space $H$given by $$\begin{array}{c}{u}_{tt}+M\left(\left[u\right]\right)Au-{\int }_0^{t}g(t-\tau )N\left(\left[u\right]\right)Aud\tau =0,\text{in}{L}^2(0,T;H)\\ u\left(0\right)=u_0,u_t\left(0\right)=u_1\end{array}$$ where by$\left[u\left(t\right)\right]$we are denoting $$\left[u\left(t\right)\right]=\left((u\left(t\right),u_t\left(t\right),(Au\left(t\right),u_t\left(t\right)),\parallel A^{\frac{1}{2}}u\left(t\right){\parallel }^2,\parallel A^{\frac{1}{2}}{u}_t\left(t\right){\parallel }^2,\parallel Au\left(t\right){\parallel }^2\right)\in {ℝ}^5$$$ A : D ⁢... Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems Irena Pawłow, Antoni Żochowski (2003) Banach Center Publications A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution. Existence and uniqueness for wave propagation in inhomogeneous elastic solids Giacomo Caviglia, Angelo Morro (2002) Rendiconti del Seminario Matematico della Università di Padova Existence and uniqueness of solutions for a three-dimensional thermoelastic system [Book] Irena Pawłow, Antoni Żochowski (2002) Existence of a solution for a nonlinearly elastic plane membrane “under tension” Daniel Coutand (1999) ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique Existence of a solution for a nonlinearly elastic plane membrane “under tension” Daniel Coutand (2010) ESAIM: Mathematical Modelling and Numerical Analysis A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of ℝ 3 , is equivalent to finding the critical points... Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions Sergio Conti, Georg Dolzmann, Bernd Kirchheim (2007) Annales de l'I.H.P. Analyse non linéaire Existence of Rayleigh resonances exponentially close to the real axis G. Vodev (1997) Annales de l'I.H.P. Physique théorique Existence of solutions for degenerate sweeping processes. Kunze, M., Monteiro Marques, Manuel D.P. (1997) Journal of Convex Analysis Existence Result for the Displacement Field of Elastic Body Ivan Šestak, Boško Jovanović (1998) Publications de l'Institut Mathématique Existence theorem in the linear theory of multipolar elasticity Carmen Maria Ieşan (1973) Aplikace matematiky Explicit solutions of the basic boundary value problems of statics of the elastic mixture theory for an annulus. Basheleishvili, M. (2004) Georgian Mathematical Journal Extended Hashin-Shtrikman variational principles Petr Procházka, Jiří Šejnoha (2004) Applications of Mathematics Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the... Extended irreversible thermodynamics in hypoelasticity Sebastiano Giambò, Annunziata Palumbo (1988) Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni The constitutive equations of rate type for a class of thermo-hypo-elastic materials are derived within the framework of the extended irreversible thermodynamics. Currently displaying 21 – 35 of 35 Previous Page 2 $