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We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . 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 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...
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...
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.
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.
A short survey of available existence results for dynamic contact problems including heat generation and heat transfer is presented.
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.
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...
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 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.
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.
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