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An asymptotically optimal model for isotropic heterogeneous linearly elastic plates

Ferdinando Auricchio, Carlo Lovadina, Alexandre L. Madureira (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction...

An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes

Sergey Grosman (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one...

Analysis of the accuracy and convergence of equation-free projection to a slow manifold

Antonios Zagaris, C. William Gear, Tasso J. Kaper, Yannis G. Kevrekidis (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the mth member of the class of algorithms ( m = 0 , 1 , ... ) finds iteratively an approximation of the appropriate zero of the (m+1)st...

Analysis of total variation flow and its finite element approximations

Xiaobing Feng, Andreas Prohl (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...

Analysis of total variation flow and its finite element approximations

Xiaobing Feng, Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since...

Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires

Franck Sueur (2006)

Annales de l’institut Fourier

On s’intéresse à des systèmes symétriques hyperboliques multidimensionnels en présence d’une semilinéarité. Il est bien connu que ces systèmes admettent des solutions discontinues, régulières de part et d’autre d’une hypersurface lisse caractéristique de multiplicité constante. Une telle solution u 0 étant donnée, on montre que u 0 est limite quand ε → 0 de solutions ( u ε ) ε ∈ ] 0 , 1 ] du système perturbé par une viscosité de taille ε . La preuve utilise un problème mixte parabolique et des développements de couches limites....

Approximation of the viscosity solution of a Hamilton-Jacobi problem.

P. Fabrie, P. Rasetarinera (1996)

Revista Matemática de la Universidad Complutense de Madrid

In this paper, a mathematical analysis of in-situ biorestoration is presented. Mathematical formulation of such process leads to a system of non-linear partial differential equations coupled with ordinary differential equations. First, we introduce a notion of weak solution then we prove the existence of at least one such a solution by a linearization technique used in Fabrie and Langlais (1992). Positivity and uniform bound for the substrates concentration is derived from the maximum principle...

Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass

C. Castro (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a hybrid, one-dimensional, linear system consisting in two flexible strings connected by a point mass. It is known that this system presents two interesting features. First, it is well posed in an asymmetric space in which solutions have one more degree of regularity to one side of the point mass. Second, that the spectral gap vanishes asymptotically. We prove that the first property is a consequence of the second one. We also consider a system in which the point mass is replaced...

Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems

Francesca De Marchis, Isabella Ianni, Filomena Pacella (2015)

Journal of the European Mathematical Society

We consider the semilinear Lane–Emden problem where p > 1 and Ω is a smooth bounded domain of ℝ 2 . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of ( p ) , as p → + ∞ . Among other results we show, under some symmetry assumptions on Ω , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p → + ∞ , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville...

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