This paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition. The argument presented makes use of the global inverse theorem and Galerkin’s method. c © 2007 Elsevier Ltd. All rights reserved.

Non-welded interfaces can be treated as a displacement discontinuity characterized by elastic stiffnesses. Applying this boundary condition to a generalized Rayleigh wave, it is shown that a fast and a slow dispersive wave can propagate along the fracture, even when the seismic properties of the rock on each side are identical.

This work deals with the derivation of a novel transparent boundary condition (TBC) for the coupling of the standard “parabolic” equation (SPE) in underwater acoustics (assuming cylindrical symmetry) with an elastic parabolic equation (EPE) for modelling the sea bottom extending hereby the existing TBCs for a fluid model of the seabed.

We present a rather simple proof of the existence of resonant frequencies for the direct scattering problem associated to a system of elastic wave equations with Dirichlet boundary condition. Our approach follows techniques similar to those in Cortés-Vega (2003). The proposed technique relies on a stationary approach of resonant frequencies, that is, the poles of the analytic continuation of th...

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. LAGNESE, Boundary Stabilization of Twin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case—where rotational forces are neglected—in [Z. ...

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [KT06] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.