Search results for "Boundary"

A class of shear deformable isotropic elastic plates with parametrically variable warping shapes

2017

A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …

Dimension estimates for the boundary of planar Sobolev extension domains

2020

We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.

Recent progress in electrical impedance tomography

2003

We consider the inverse problem of finding cavities within some body from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We survey two algorithms for solving this inverse problem, namely the factorization method and a MUSIC-type algorithm. In particular, we present a number of numerical results to highlight the potential and the limitations of these two methods.

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

2012

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

A boundary min-max principle as a tool for boundary element formulations

1991

Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996

Porous medium equation with absorption and a nonlinear boundary condition

2002

where is a bounded domain with smooth boundary, @=@ is the outer normal derivative, m ? 1; p; and q are positive parameters and u0 is in L∞( ). Problems of this form arise in mathematical models in a number of areas of science, for instance, in models for gas or :uid :ow in porous media [3] and for the spread of certain biological populations [13]. In the semilinear case (that is for m=1), there is an extensive literature about global existence and blow-up results for this type of problems, see among others, [5,9,16] and the literature therein. For the degenerate case (that is for m = 1), with a nonlinear boundary condition, local existence and uniqueness of weak solutions which are limit o…

On a global superconvergence of the gradient of linear triangular elements

1987

Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.

Existence and Singularities for the Prandtl Boundary Layer Equations

2000

Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.

ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS

2004

A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially f…