Related papers: Variations of thin piezoelectric shallow shells: T…
In this article, we describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm…
We study the PDE $\lambda_j(D^2 u) = 0$, in $\Omega$, with $u=g$, on $\partial \Omega$. Here $\lambda_1(D^2 u) \leq ... \leq \lambda_N (D^2 u)$ are the ordered eigenvalues of the Hessian $D^2 u$. First, we show a geometric interpretation of…
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
The duality approach in 2-{\it dim} two-component regular checkerboards was extended onto piezoelectricity and piezomagnetism problems. There are found a relation for effective piezoelectric and piezomagnetic modules for the checkerboard…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
There are many numerical methods for simulate three-dimensional photonic crystals, after comparison, we choose Yee's scheme to be our discrete method. So far, this method can only be applied to simple cubic lattice and face-centered cubic…
We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…
We analyze the three-dimensional buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Peclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal…
We investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero. We identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number…
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher…
Using a geometrically motivated 8-parameter ansatz through the thickness, we reduce a three-dimensional shell-like geometrically nonlinear Cosserat material to a fully two-dimensional shell model. Curvature effects are fully taken into…
We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of…
This paper is a brief account of the Steklov eigenvalue problem on a 2-dimensional rectangular domain, and then on a 3-dimensional rectangular box. It is divided into four sections. Section 1 relies heavily on real analytic methods to show…
Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational…
In this paper we deduce by {\Gamma}-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we study the case…
An eigenvalue problem arising in optimal insulation related to the minimization of the heat decay rate of an insulated body is adapted to enforce a positive lower bound imposed on the distribution of insulating material. We prove the…
Self-similar solutions of the so called Airy equations, equivalent to the dispersionless nonlinear Schr\"odinger equation written in Madelung coordinates, are found and studied from the point of view of complete integrability and of their…