English
Related papers

Related papers: A Novel Approach to Elastodynamics: I. The Two-Dim…

200 papers

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…

Classical Physics · Physics 2022-01-31 Nadezhda I. Aleksandrova

Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent…

Classical Physics · Physics 2022-11-15 Stéphane André , Camille Noûs

Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element…

Numerical Analysis · Mathematics 2022-04-07 A. Aimi , M. Diligenti , M. L. Sampoli , A. Sestini

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…

Analysis of PDEs · Mathematics 2010-08-20 H. Beirão da Veiga , F. Crispo , C. R. Grisanti

An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the…

Dynamical Systems · Mathematics 2025-09-15 Xijun Hu , Yuwei Ou , Jiexin Sun

We study free boundary problems for incompressible inhomogeneous flows governed by the Navier--Stokes equations, focusing on the regularity and global-in-time well-posedness of solutions in critical functional frameworks for small initial…

Analysis of PDEs · Mathematics 2025-12-11 Piotr B. Mucha , Tomasz Piasecki , Yoshihiro Shibata

Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…

Analysis of PDEs · Mathematics 2016-04-26 Y. A. Antipov

A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…

Numerical Analysis · Mathematics 2023-10-10 Uditnarayan Kouskiya , Amit Acharya

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…

Materials Science · Physics 2023-01-19 Benjamin C. Cameron , Cem Tasan

This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a…

Analysis of PDEs · Mathematics 2018-02-28 M. Latorre , S. Segura de León

We present a new analytical and numerical framework for solution of Partial Differential Equations (PDEs) that is based on an exact transformation that moves the boundary constraints into the dynamics of the corresponding governing…

Numerical Analysis · Mathematics 2023-02-14 Yulia T. Peet , Matthew M. Peet

The aim of this study is to present a reliable combination of the differential transformation method (DTM) and Pad\'e approximants to make, for the first time, a semi-analytic analysis of the problem of free convection boundary-layer flow…

Numerical Analysis · Mathematics 2012-12-10 Haldun Alpaslan Peker , Galip Oturanc

The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…

Optimization and Control · Mathematics 2022-07-22 Georgy Kostin , Alexander Gavrikov

We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…

Analysis of PDEs · Mathematics 2026-05-20 Andreas Chatziafratis , Alain Miranville , Tohru Ozawa

We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…

Dynamical Systems · Mathematics 2021-04-23 Matteo Gallone , Stefano Pasquali

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided…

Analysis of PDEs · Mathematics 2021-05-28 George C. Hsiao , Tonatiuh Sánchez-Vizuet

We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…

Numerical Analysis · Mathematics 2016-05-24 Christoph Erath , Robert Schorr

We study two types of asymptotic problems whose common feature - and difficulty- is to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for…

Analysis of PDEs · Mathematics 2012-05-22 Guy Barles , Elisabeth Mironescu

A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method with the method of images and with the classical integral…

Condensed Matter · Physics 2007-05-23 Athanassios S. Fokas , Daniel ben-Avraham