Page 1 Next

Displaying 1 – 20 of 89

Showing per page

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 mixed-type equations in domains with multiply connected hyperbolicity subdomains.

Sibirskij Matematicheskij Zhurnal

A finite element method for the nonlinera Tricomi problem.

Numerische Mathematik

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 simple bioclogging model that accounts for spatial spreading of bacteria.

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

About one high-order linear equation of mixed type.

Sibirskij Matematicheskij Zhurnal

About the decay of surface waves on viscous fluids without surface tension

Banach Center Publications

We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...

Application of complex analysis to second order equations of mixed type

Annales Polonici Mathematici

This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral...

Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach

ESAIM: Control, Optimisation and Calculus of Variations

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations ${\partial }_{t}\left({r}_{h}u\right)-\mathrm{div}\left({a}_{h}·Du\right)$ with ${r}_{h}\left(x,t\right)\ge 0$, ${r}_{h}\in {L}^{\infty }\left(\Omega ×\left(0,T\right)\right)$. The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain G-convergence for elliptic operators $\left({r}_{h}\equiv 0\right)$, G-convergence for parabolic operators $\left({r}_{h}\equiv 1\right)$, singular perturbations of an elliptic operator $\left({a}_{h}\equiv a$ and ${r}_{h}\to r$, possibly $r\equiv 0\right)$.

Asymptotic representations for solutions of bisingular problems.

Memoirs on Differential Equations and Mathematical Physics

Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains.

Journal of Inequalities and Applications [electronic only]

Boundary value problems for some classes of degenerating second order partial differential equations.

Memoirs on Differential Equations and Mathematical Physics

Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

Open Mathematics

In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations...

Convergence d'un schéma de type éléments finis-volumes finis pour un système formé d'une équation elliptique et d'une équation hyperbolique

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

Convergence of a finite volume scheme for an elliptic-hyperbolic system

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

Page 1 Next