Journal ArticleDOI
A Gronwall inequality for weakly Lipschitzian mappings
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1992-11-01. It has received 10 citations till now. The article focuses on the topics: Gronwall's inequality & Concave function.read more
Citations
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Journal ArticleDOI
Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity
TL;DR: In this article, the initial-boundary value problem for the time-dependent Ginzburg-Landau equations that model the macroscopic behavior of superconductors is considered and the convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme.
Journal ArticleDOI
Local invertibility of Sobolev functions
Irene Fonseca,Wilfrid Gangbo +1 more
TL;DR: In this paper, a local inverse function theorem is established for mappings $v \in W^{1,N} (\Omega,\mathbb{R}^N )$, $\Omega \subset \mathbb {R} N $ open set, such that $det
abla v(x) > 0$ almost everywhere in $x \in \Omega $.
Journal Article
On the weak lower semicontinuity of energies with polyconvex integrands
TL;DR: In this paper, it was shown that if / is continuous and F(u) := fK \det(Vu(x))\dx where if is a compact set, then F is weakly lower semicontinuous in W, N > p > N − 1 if and only if mea$(dK) = 0.
Journal ArticleDOI
Constitutive Laws for Pseudo-Elastic Materials
Deborah Brandon,Robert C. Rogers +1 more
TL;DR: In this article, a new model of pseudo-elastic materials based on experimental obser-vations of one-dimensional motions of SM A materials is introduced, which incorporates phase fractions as an internal variable and allows for both reversible (elastic) and irreversible (plastic) modes inside the hysteresis loop.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
On thermodynamics and elastic-plastic materials
Bernard D. Coleman,David R. Owen +1 more
Book
A First Course in the Mathematical Foundations of Thermodynamics
TL;DR: In this paper, a modern treatment of the Second Law of Energy and Entropy for thermodynamic systems has been proposed, based on the Clausius property and the conservation property of the Dissipation property.
Journal ArticleDOI
Weakly Decaying Energy Separation and Uniqueness of Motions of an Elastic-Plastic Oscillator with Work-Hardening
TL;DR: In this paper, the authors consider the case of an elastic-perfectly plastic element, where there is an upper bound for the magnitude of the force that the element can provide.
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