English
Related papers

Related papers: A non-convex variational problem appearing in a la…

200 papers

We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $\Omega \subseteq \mathbb{R}^n$. Specifically, we show that if…

Analysis of PDEs · Mathematics 2026-04-16 Michele Gatti , Julian Scheuer , Tobias Weth

We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…

Differential Geometry · Mathematics 2008-11-18 Szu-yu Sophie Chen

We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can…

Analysis of PDEs · Mathematics 2023-09-13 Dominik Engl , Stefan Krömer , Martin Kružík

Large deviation estimates for the following linear parabolic equation are studied: \[ \frac{\partial u}{\partial t}=\tr\Big(a(x)D^2u\Big) + b(x)\cdot D u + \int_{\R^N} \Big\{(u(x+y)-u(x)-(D u(x)\cdot y)\ind{|y|<1}(y)\Big\}\d\mu(y), \] where…

Analysis of PDEs · Mathematics 2009-09-09 Cristina Brändle , Emmanuel Chasseigne

In an earlier work made by the first author with J. Turi (Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008), the solution of a stochastic variational inequality modeling an…

Analysis of PDEs · Mathematics 2011-12-21 Alain Bensoussan , Laurent Mertz

This work is focused on the longtime behavior of a non linear evolution problem describing the vibrations of an extensible elastic homogeneous beam resting on a viscoelastic foundation with stiffness k>0 and positive damping constant.…

Mathematical Physics · Physics 2011-02-08 Ivana Bochicchio , Elena Vuk

A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution…

Analysis of PDEs · Mathematics 2024-07-15 Siddharth Singh , Janusz Ginster , Amit Acharya

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of…

Differential Geometry · Mathematics 2021-09-01 Christian Baer , Bernhard Hanke

Tangent stabilised large strain isotropic elasticity was recently proposed by Poya et al. [1] wherein by working directly with principal stretches the entire eigenstructure of constitutive and geometric/initial stiffness terms were found in…

Computational Physics · Physics 2024-09-30 Roman Poya , Rogelio Ortigosa , Antonio J. Gil , Theodore Kim , Javier Bonet

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson

A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…

Mathematical Physics · Physics 2024-09-19 Roman Cherniha , Vasyl' Davydovych , Joanna Stachowska-Pietka , Jacek Waniewski

In this article we develop a new primal dual variational formulation suitable for a large class of non-convex problems in the calculus of variations. The results are obtained through basic tools of convex analysis, duality theory, the…

Optimization and Control · Mathematics 2019-09-05 Fabio Botelho

A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the…

Analysis of PDEs · Mathematics 2023-06-27 Willem J. M. van Oosterhout , Matthias Liero

Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…

Analysis of PDEs · Mathematics 2021-06-03 Calum Rickard , Mahir Hadzic , Juhi Jang

This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method…

Functional Analysis · Mathematics 2017-06-21 Maria Gokieli , Nobuyuki Kenmochi , Marek Niezgódka

In this paper, we are concerned with the Cauchy problem for isentropic gas dynamics. Through the contribution of many researchers such as Lax, P. D., Glimm, J., DiPerna, R. J. and Liu, T. P., the decay of solutions was established. They…

Analysis of PDEs · Mathematics 2023-01-04 Naoki Tsuge

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…

Analysis of PDEs · Mathematics 2010-10-22 Xianpeng Hu , Dehua Wang

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…

Mathematical Physics · Physics 2017-06-30 J. Weberszpil , J. A. Helayël-Neto

In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system…

Numerical Analysis · Mathematics 2024-01-02 Piotr Bartman , Krzysztof Bartosz , Michał Jureczka , Paweł Szafraniec