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Dynamics and patterns of an activator-inhibitor model with cubic polynomial source

Yanqiu Li, Juncheng Jiang (2019)

Applications of Mathematics

The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the...

Dynamics of a Lotka-Volterra map

Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre (2006)

Fundamenta Mathematicae

Given the plane triangle with vertices (0,0), (0,4) and (4,0) and the transformation F: (x,y) ↦ (x(4-x-y),xy) introduced by A. N. Sharkovskiĭ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior...

Dynamics of a modified Davey-Stewartson system in ℝ³

Jing Lu (2016)

Colloquium Mathematicae

We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system i u + Δ u = λ | u | u + λ b u v x , - Δ v = b ( | u | ² ) x . Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].

Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions

David Hoff (2001)

Journées équations aux dérivées partielles

We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...

Dynamique des points vortex dans une équation de Ginzburg-Landau complexe

Evelyne Miot (2009/2010)

Séminaire Équations aux dérivées partielles

On considère une équation de Ginzburg-Landau complexe dans le plan. On étudie un régime asymptotique à petit paramètre dans lequel les solutions comportent des singularités ponctuelles, appelées points vortex, et on détermine un système d’équations différentielles ordinaires du premier ordre décrivant la dynamique de ces points jusqu’au premier temps de collision.

EasyMSG : tools and techniques for an adaptive overlapping in SPMD programming

Pascal Havé (2002)

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

During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this techniques...

EasyMSG: Tools and techniques for an adaptive overlapping in SPMD programming

Pascal Havé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this...

Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi, Lucia Gastaldi (2002)

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

In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L 2 norm for the sequence of discrete operators....

Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi, Lucia Gastaldi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L2 norm for the sequence of discrete...

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the...

Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the...

Effective Hamiltonians and Quantum States

Lawrence C. Evans (2000/2001)

Séminaire Équations aux dérivées partielles

We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function u solving the eikonal equation aėȧnd a probability measure σ solving a related transport equation.We present some elementary formal identities relating certain quantum states ψ and u , σ . We show also how to build out of u , σ an approximate...

Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields

Georgi D. Raikov (1999)

Annales de l'institut Fourier

We consider the Pauli operator H ( μ ) : = j = 1 m σ j - i x j - μ A j 2 + V selfadjoint in L 2 ( m ; 2 ) , m = 2 , 3 . Here σ j , j = 1 , ... , m , are the Pauli matrices, A : = ( A 1 , ... , A m ) is the magnetic potential, μ > 0 is the coupling constant, and V is the electric potential which decays at infinity. We suppose that the magnetic field generated by A satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case m = 3 , its direction is constant. We investigate the asymptotic behaviour as μ of the number of the eigenvalues of H ( μ ) smaller than...

Currently displaying 801 – 820 of 3659