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### 1 Structure de contact et équations aux dérivées partielles d'après V. V. Lychagin

Publications du Département de mathématiques (Lyon)

### 3D-2D asymptotic analysis for micromagnetic thin films

ESAIM: Control, Optimisation and Calculus of Variations

$\Gamma$-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness $\epsilon$ approaches zero of a ferromagnetic thin structure ${\Omega }_{\epsilon }=\omega ×\left(-\epsilon ,\epsilon \right)$, $\omega \subset {ℝ}^{2}$, whose energy is given by${ℰ}_{\epsilon }\left(\overline{m}\right)=\frac{1}{\epsilon }{\int }_{{\Omega }_{\epsilon }}\left(W\left(\overline{m},\nabla \overline{m}\right)+\frac{1}{2}\nabla \overline{u}·\overline{m}\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$subject to$\text{div}\left(-\nabla \overline{u}+\overline{m}{\chi }_{{\Omega }_{\epsilon }}\right)=0\phantom{\rule{1.0em}{0ex}}\text{on}{ℝ}^{3},$and to the constraint$|\overline{m}|=1\text{on}{\Omega }_{\epsilon },$where $W$ is any continuous function satisfying $p$-growth assumptions with $p>1$. Partial results are also obtained in the case $p=1$, under an additional assumption on $W$.

### 3D-2D Asymptotic Analysis for Micromagnetic Thin Films

ESAIM: Control, Optimisation and Calculus of Variations

Γ-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure ${\Omega }_{\epsilon }=\omega ×\left(-\epsilon ,\epsilon \right)$, $\omega \subset {ℝ}^{2}$, whose energy is given by ${ℰ}_{\epsilon }\left(\overline{m}\right)=\frac{1}{\epsilon }{\int }_{{\Omega }_{\epsilon }}\left(W\left(\overline{m},\nabla \overline{m}\right)+\frac{1}{2}\nabla \overline{u}·\overline{m}\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$ subject to $\text{div}\left(-\nabla \overline{u}+\overline{m}{\chi }_{{\Omega }_{\epsilon }}\right)=0\phantom{\rule{1.0em}{0ex}}\phantom{\rule{4.0pt}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}{ℝ}^{3},$ and to the constraint $|\overline{m}|=1\phantom{\rule{4.0pt}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}{\Omega }_{\epsilon },$ where W is any continuous function satisfying p-growth assumptions with p> 1. Partial results are also obtained in the case p=1, under an additional assumption on W.

### 4D Embryogenesis image analysis using PDE methods of image processing

Kybernetika

In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely...

### A blow-up mechanism for a chemotaxis model

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...

### A Cauchy problem for ${u}_{t}-\Delta u={u}^{p}\phantom{\rule{4pt}{0ex}}\text{with}\phantom{\rule{4pt}{0ex}}0<p<1$. Asymptotic behaviour of solutions

Annales de la Faculté des sciences de Toulouse : Mathématiques

### A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Czechoslovak Mathematical Journal

Given a domain $\Omega$ of class ${C}^{k,1}$, $k\in ℕ$, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega$ in the sense that $\left(\partial -\partial {x}_{n}\right)\alpha \left({x}^{\text{'}},0\right)=-N\left({x}^{\text{'}}\right)$ and that still is of class ${C}^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class ${C}^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.

### A class of pseudo differential operators with multiple non-involutive characteristics

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A control on the set where a Green's function vanishes

Colloquium Mathematicae

### A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity.

International Journal of Mathematics and Mathematical Sciences

### A Direct Approach to the Mellin Transform.

The journal of Fourier analysis and applications [[Elektronische Ressource]]

### A discrete phenomenon in propagation of ${C}^{\infty }$ singularities

Banach Center Publications

### A field equation defined by a Hurwitz pair

Proceedings of the Winter School "Geometry and Physics"

### A Finite-Difference Approximation for the Eigenvalue of the Clamped Plate.

Numerische Mathematik

### A free boundary problem for the $p$-Laplacian: uniqueness, convexity, and successive approximation of solutions.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation

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

We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...

### A general approach for multiconfiguration method sin quantum molecular chemistry

Annales de l'I.H.P. Analyse non linéaire

### A general class of phase transition models with weighted interface energy

Annales de l'I.H.P. Analyse non linéaire

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