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Displaying 121 – 140 of 734

Branching random motions, nonlinear hyperbolic systems and travellind waves

Nikita Ratanov (2006)

ESAIM: Probability and Statistics

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation via such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal...

Caractérisation d'opérateurs pseudodifférentiels et applications (d'après R. Beals)

A. Grigis (1975/1976)

Séminaire Équations aux dérivées partielles (Polytechnique)

Cascade of phases in turbulent flows

Christophe Cheverry (2006)

Bulletin de la Société Mathématique de France

This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.

Characteristic Cauchy problems and solutions of formal power series

Sunao Ouchi (1983)

Annales de l'institut Fourier

Let $L (z, \partial_{z}) = (\partial_{z_{0}})^{k} - A (z, \partial_{z})$ be a linear partial differential operator with holomorphic coefficients, where $A (z, \partial_{z}) = \sum_{j = 0}^{k - 1} A_{j} (z, \partial_{z^{'}}) (\partial_{z_{0}})^{j}, ord . A (z, \partial_{z}) = m > k$ and $z = (z_{0}, z^{'}) \in C^{n + 1} .$ We consider Cauchy problem with holomorphic data $L (z, \partial_{z}) u (z) = f (z), (\partial_{z_{0}})^{i} u (0, z^{'}) = {\hat{u}}_{i} (z^{'}) (0 \leq i \leq k - 1) .$ We can easily get a formal solution $\hat{u} (z) = \sum_{n = 0}^{\infty} {\hat{u}}_{n} (z^{'}) (z_{0})^{n} / n!$ , bu in general it diverges. We show under some conditions that for any sector $S$ with the opening less that a constant determined by $L (z, \partial_{z})$ , there is a function $u_{S} (z)$ holomorphic except on ${z_{0} = 0}$ such that $L (z, \partial_{z}) u_{S} (z) = f (z)$ and $u_{S} (z) \sim \hat{u} (z)$ as $z_{0} \to 0$ in $S$ .

Characterization of the solutions of a 2b-parabolic operator with initial data in BMO

A. Grimaldi, F. Ragnedda (1983)

Annales Polonici Mathematici

Classical solutions of the two-phase Stefan-type problem

Józef Osada (1987)

Colloquium Mathematicae

Closed form solutions of iterative functional differential equations.

Li, Wenrong, Cheng, Sui Sun, Lu, Tzon Tzer (2001)

Applied Mathematics E-Notes [electronic only]

Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I : Résultats généraux pour le problème de Dirichlet

Monique Dauge, Serge Nicaise, Maryse Bourlard, Jean Mbaro-Saman Lubuma (1990)

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

Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack.

Chikouche, Wided, Aibèche, Aissa (2003)

International Journal of Mathematics and Mathematical Sciences

Coefficients of the singularities on domains with conical points

Monique Dauge, Serge Nicaise (1992)

Banach Center Publications

As a model for elliptic boundary value problems, we consider the Dirichlet problem for an elliptic operator. Solutions have singular expansions near the conical points of the domain. We give formulas for the coefficients in these expansions.

Coherent and focusing multidimensional nonlinear geometric optics

J.-L. Joly, G. Métivier, J. Rauch (1995)

Annales scientifiques de l'École Normale Supérieure

Coherent nonlinear waves and the Wiener algebra

Guy Métivier, Jean-Luc Joly, Jeffrey Rauch (1994)

Annales de l'institut Fourier

We study oscillatory solutions of semilinear first order symmetric hyperbolic system $L u = f (t, x, u, \overline{u})$ , with real analytic $f$ .The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in $T, X$ with only the natural hypothesis of coherence.In the special case where $L$ has constant coefficients and the phases are linear, the solutions have asymptotic description $u^{ϵ} = U (t, x, t / ϵ, x / ϵ) + o (1)$ where the profile $U (t, x, T, X)$ is almost periodic in $(T, X)$ .The main novelty in the analysis is the space of profiles which...

Common general practical method for solving ordinary and partial differential equations

K. Orlov (1979)

Matematički Vesnik

Comparison of differential representations for radially symmetric Stokes flow.

Dassios, George, Vafeas, Panayiotis (2004)

Abstract and Applied Analysis

Comparison of exact and approximate causal solutions of a model curved-space wave equation

James L. Anderson, William J. Heyl (1984)

Annales de l'I.H.P. Physique théorique

Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods

Denis Borisov, Giuseppe Cardone (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...

Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods*

Denis Borisov, Giuseppe Cardone (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Comportement d'une plaque élastique dont une petite région est rigide et animée d'un mouvement vibratoire. Étude asymptotique de la matrice d'impédance

Campbell Alain, Nazarov Sergueï (1995)

Annales de la Faculté des sciences de Toulouse : Mathématiques

COMPUTATION of generalized stress intensity factors for bonded elastic structures

Marius Bochniak, Anna–Margarete Sändig (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities....

Computation of radial solutions of semilinear equations.

Korman, P. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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