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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...
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...
So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
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
()
finds iteratively
an approximation
of the appropriate zero
of the (m+1)st...
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 , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...
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...
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 étant donnée, on montre que est limite quand de solutions du système perturbé par une viscosité de taille . La preuve utilise un problème mixte parabolique et des développements de couches limites....
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...
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...
We consider the semilinear Lane–Emden problem where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of , as . Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as , 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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