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On the structure of layers for singularly perturbed equations in the case of unbounded energy

E. Sanchez–Palencia (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...

On the structure of symmetric 2 x 2 gradients.

Pablo Pedregal (2003)

RACSAM

A way of geometrically representing symmetric 2 × 2-gradients is proposed, and a general theorem characterizing sets of gradients is proved. We believe this perspective may help in understanding the structure of gradients and visualizing it. Several non-trivial examples are discussed.

On the theory of thermoelasticity

Henryk Kołakowski, Jarosław Łazuka (2011)

Applicationes Mathematicae

The aim of this paper is to prove some properties of the solution to the Cauchy problem for the system of partial differential equations describing thermoelasticity of nonsimple materials proposed by D. Iesan. Explicit formulas for the Fourier transform and some estimates in Sobolev spaces for the solution of the Cauchy problem are proved.

On the two-step iterative method of solving frictional contact problems in elasticity

Todor Angelov, Asterios Liolios (2005)

International Journal of Applied Mathematics and Computer Science

A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.

On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation

F. Ben Belgacem, C. Bernardi, A. Blouza, M. Vohralík (2009)

Mathematical Modelling of Natural Phenomena

The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem...

On two-scale convergence and related sequential compactness topics

Anders Holmbom, Jeanette Silfver, Nils Svanstedt, Niklas Wellander (2006)

Applications of Mathematics

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2 ( Ω ) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.

Onde sferiche in termoelasticità lineare

Antonino Valenti (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

After writing the equations which characterize the thermomechanics of hyperelastic continua subject to small transformations according to a recent hypothesis on the heat flux vector, we study the spherical thermomechanical waves.

Ondes de surface faiblement non-linéaires

Sylvie Benzoni-Gavage, Jean-François Coulombel, Nikolay Tzvetkov (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

Cet exposé concerne l’approximation faiblement non-linéaire de problèmes aux limites invariants par changement d’échelles.

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