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Displaying 901 – 920 of 2227

Is GPU the future of Scientific Computing ?

Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Perignon, Christophe Picard, Florian De Vuyst, Christophe Labourdette (2013)

Annales mathématiques Blaise Pascal

These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay),...

Jumping nonlinearities and mathematical models of suspension bridge

Pavel Drábek (1994)

Acta Mathematica et Informatica Universitatis Ostraviensis

Justification de l'optique géométrique non linéaire pour un système de lois de conservation

C. Cheverry (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

Justification of the steepest descent method for the integral statement of an inverse problem for a hyperbolic equation.

Kabanikhin, S.I., Iskakov, K.T. (2001)

Sibirskij Matematicheskij Zhurnal

KAM theory for the hamiltonian derivative wave equation

Massimiliano Berti, Luca Biasco, Michela Procesi (2013)

Annales scientifiques de l'École Normale Supérieure

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.

Kelvin principle for a class of singular equations.

Altin, Abduhllah, Young, Eutiquio C. (1989)

International Journal of Mathematics and Mathematical Sciences

Kinetic approach to systems of conservation laws

Benoît Perthame (1992)

Journées équations aux dérivées partielles

Kinetic formulation for heterogeneous scalar conservation laws

Anne-Laure Dalibard (2006)

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

Kink-antikink interaction for semilinear wave equations with a small parameter.

Garcia, Martin G., Omel'yanov, Georgii A. (2009)

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

Kirchhoff-Carrier elastic strings in noncylindrical domains.

Limaco Ferrel, J., Medeiros, L.A. (1999)

Portugaliae Mathematica

Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

This work is concerned with the proof of $L_{p} - L_{q}$ decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation $u_{t t} - λ^{2} (t) b^{2} (t) (Δ u - m^{2} u) = 0$ . The coefficient consists of an increasing smooth function $λ$ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, $m^{2}$ is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).

Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces

Slavík, Jakub (2017)

Proceedings of Equadiff 14

We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.

$L^{1}$ singular limit for relaxation and viscosity approximations of extended traffic flow models.

Klingenberg, Christian, Lu, Yunguang, Zhao, Huijiang (2003)

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

$L^{1}$ stability of conservation laws for a traffic flow model.

Li, Tong (2001)

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

$L^{2}$ -type contraction for systems of conservation laws

Denis Serre, Alexis F. Vasseur (2014)

Journal de l’École polytechnique — Mathématiques

The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in $L^{1}$ . However it is not a contraction in $L^{p}$ for any $p > 1$ . Leger showed in [20] that for a convex flux, it is however a contraction in $L^{2}$ up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...

$L^{2}$ well-posed Cauchy problems and symmetrizability of first order systems

Guy Métivier (2014)

Journal de l’École polytechnique — Mathématiques

The Cauchy problem for first order system $L (t, x, \partial_{t}, \partial_{x})$ is known to be well-posed in $L^{2}$ when it admits a microlocal symmetrizer $S (t, x, ξ)$ which is smooth in $ξ$ and Lipschitz continuous in $(t, x)$ . This paper contains three main results. First we show that a Lipschitz smoothness globally in $(t, x, ξ)$ is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is equivalent to the existence of full symmetrizers having the same smoothness. This notion was first introduced in [FL67]. This is the key point...

$L_{2} (Σ)$ -regularity of the boundary to boundary operator $B^{*} L$ for hyperbolic and Petrowski PDEs.

Lasiecka, I., Triggiani, R. (2003)

Abstract and Applied Analysis

$L^{\infty} - L^{2}$ weighted estimate for the wave equation with potential

Vladimir Georgiev, Nicola Visciglia (2003)

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

We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential $V \geq 0$ satisfies $|V (x)| \leq \frac{C}{{(1 + |x|)}^{2 + ϵ_{0}}},$ where $ϵ_{0} > 0$ .

$L^{p}$ -decay of solutions to dissipative-dispersive perturbations of conservation laws

Grzegorz Karch (1997)

Annales Polonici Mathematici

We study the decay in time of the spatial $L^{p}$ -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.

$L^{p}$ -estimates for hyperbolic operators applications to $□ u = u^{k}$

I. Peral, J. C. Peral, M. Walias (1982)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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