In this note we formulate a sufficient condition for the quasiconvexity at x 7→ λx of certain functionals I(u) which model the stored-energy of elastic materials subject to a deformation u. The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to Müller and Spector, on admissible deformations. Deformations obey the condition u(x) = λx whenever x ...

The morphological evolution during spinodal decomposition of a binary alloy thin film elastically constrained by a substrate is studied. Elastic solutions, derived for elastically anisotropic thin films subject to the mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phase-field model. The Cahn–Hilliard diffusion equation for a thin film boundary conditio...

This paper proves sharp inequalities for the frequencies of vibration of strings and cylindrical membranes, under either fixed or fixed-free boundary conditions. We establish such inequalities also on the "generalized" cylinder, which is the cross-product of an interval with a homogeneous Riemannian manifold. The goal is to better understand the effect that inhomogeneities in the mass distribut...

Controllability properties of a partial di erential equation (PDE) model describing a thermoelastic plate are studied. The PDE is comprised of a Kircho plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by > 0. Boundary control is exerted through the (two) free bounda...

In this article, we study the classical solution of mixed problem in a quarter plane for one-dimensional wave equation. This models propagation displacement waves during longitudinal impact on bar, when load remains contact with bar and has linear elastic element at end. On lower boundary, Cauchy conditions are specified, second them discontinuity first kind one point. The boundary condition, i...

the study of wave and its propagation on the water surface is among significant phenomena in designing quay, marine and water structures. therefore, in order to design structures which are exposed to direct wave forces, it is necessary to study and simulate water surface height and the wave forces on the structures body in different boundary conditions. in this study, the propagation of static ...

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of...

We consider a problem of reconstructing a cluster of small elastic inclusions which are located close to each other. We show that the location of the cluster and the elastic moment tensor associated with it can be reconstructed by the measurements of the displacement vectors on the boundary corresponding to the traction applied on the boundary. The detected elastic moment tensor represents the ...

<p style='text-indent:20px;'>In this paper, we study the initial boundary value problem of visco-elastic dynamical system with nonlinear source term in control system. By variational arguments and an improved convexity method, prove global nonexistence solution, also give a sharp condition for existence nonexistence.</p>