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### 2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

### 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.

### A boundary value problem for cold plasma dynamics.

Journal of Applied Mathematics

### A Boundary value Problem for Equations of mixed type

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

### A boundary value problem for mixed-type equations in domains with multiply connected hyperbolicity subdomains.

Sibirskij Matematicheskij Zhurnal

### A class of boundary problems for extremal surfaces of mixed type in Minkowski 3-space.

Journal für die reine und angewandte Mathematik

### A Convergent Finite Elemet Formulation for Transonic Flow.

Numerische Mathematik

### A Finite Element Method for a Boundary Value Problem of Mixed Type.

Numerische Mathematik

### A finite element method for the nonlinera Tricomi problem.

Numerische Mathematik

### A Finite Element Method for the Tricomi Problem.

Numerische Mathematik

### A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

ESAIM: Control, Optimisation and Calculus of Variations

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...

### A general investigation of admissible couplings between systems of higher order and different type

Banach Center Publications

### A generalization of the Hille--Yosida theorem to the case of degenerate semigroups in locally convex spaces.

Sibirskij Matematicheskij Zhurnal

### A quasi-boundary value method for regularizing nonlinear ill-posed problems.

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

### A simple bioclogging model that accounts for spatial spreading of bacteria.

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

### A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies

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

The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...

### A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...

### A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...

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