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In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…

Optimization and Control · Mathematics 2021-08-17 Bowen Yi , Ruigang Wang , Ian R. Manchester

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

Systems and Control · Computer Science 2017-02-09 Ian R. Manchester , Jean-Jacques E. Slotine

We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Elisa Davoli , Martin Kružík

The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…

Condensed Matter · Physics 2016-11-25 A. I. Leonov , V. S. Volkov

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Antonio DeSimone , Maria Giovanna Mora , Massimiliano Morini

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

Numerical Analysis · Mathematics 2018-05-01 Yue Mei , Daniel E. Hurtado , Sanjay Pant , Ankush Aggarwal

This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…

Analysis of PDEs · Mathematics 2025-10-24 Amartya Chakrabortty , Georges Griso , Julia Orlik

We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…

Classical Analysis and ODEs · Mathematics 2012-05-29 Adrien Hardy , Arno B. J. Kuijlaars

A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that the strains of minimizing sequences associated to re-scaled…

Analysis of PDEs · Mathematics 2019-07-01 Francesco Maddalena , Danilo Percivale , Franco Tomarelli

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

Analysis of PDEs · Mathematics 2023-10-23 Abramo Agosti , Robert Lasarzik , Elisabetta Rocca

Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…

Soft Condensed Matter · Physics 2013-05-23 Michel Destrade , Paul A. Martin , Tom C. T. Ting

We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic…

Analysis of PDEs · Mathematics 2018-05-18 Sylvia Anicic

We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable…

Analysis of PDEs · Mathematics 2022-01-26 Edoardo Mainini , Roberto Ognibene , Danilo Percivale

We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…

Analysis of PDEs · Mathematics 2020-09-16 Ionel-Dumitrel Ghiba , Mircea Bîrsan , Peter Lewintan , Patrizio Neff

A result concerning global extrema in a nonsmooth nonconvex variational problem that appears in applications (e.g. in a large deformation elasticity problem) is investigated in comparison with a result of D.Y. Gao and R.W. Ogden. The tools…

Optimization and Control · Mathematics 2012-02-17 M. D. Voisei , C. Zalinescu

This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…

Optimization and Control · Mathematics 2024-05-02 Y. J. J. Heuts , M. C. F. Donkers

An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…

Analysis of PDEs · Mathematics 2025-06-13 S. N. Antontsev , H. B. de Oliveira , I. V. Kuznetsov , D. A. Prokudin , Kh. Khompysh

We compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic…

Functional Analysis · Mathematics 2020-07-01 Giovanni Scilla , Bianca Stroffolini

We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable…

Optimization and Control · Mathematics 2025-03-25 Pierluigi Cesana , Edoardo Fabbrini , Marco Morandotti

In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential…

Numerical Analysis · Mathematics 2025-01-22 Georgios Grekas , Konstantinos Koumatos , Charalambos Makridakis , Andreas Vikelis