77,981 research outputs found
Unstable and Stable Galaxy Models
To determine the stability and instability of a given steady galaxy
configuration is one of the fundamental problems in the Vlasov theory for
galaxy dynamics. In this article, we study the stability of isotropic spherical
symmetric galaxy models , for which the distribution function
depends on the particle energy only. In the first part of the article, we
derive the first sufficient criterion for linear instability of
is linearly unstable if the second-order operator has a
negative direction, where is the projection onto the function
space being the angular momentum [see the explicit formula
(\ref{A0-radial})]. In the second part of the article, we prove that for the
important King model, the corresponding is positive definite. Such a
positivity leads to the nonlinear stability of the King model under all
spherically symmetric perturbations.Comment: to appear in Comm. Math. Phy
A sharp stability criterion for the Vlasov-Maxwell system
We consider the linear stability problem for a 3D cylindrically symmetric
equilibrium of the relativistic Vlasov-Maxwell system that describes a
collisionless plasma. For an equilibrium whose distribution function decreases
monotonically with the particle energy, we obtained a linear stability
criterion in our previous paper. Here we prove that this criterion is sharp;
that is, there would otherwise be an exponentially growing solution to the
linearized system. Therefore for the class of symmetric Vlasov-Maxwell
equilibria, we establish an energy principle for linear stability. We also
treat the considerably simpler periodic 1.5D case. The new formulation
introduced here is applicable as well to the nonrelativistic case, to other
symmetries, and to general equilibria
Traveling Wave Solutions of a Reaction-Diffusion Equation with State-Dependent Delay
This paper is concerned with the traveling wave solutions of a
reaction-diffusion equation with state-dependent delay. When the birth function
is monotone, the existence and nonexistence of monotone traveling wave
solutions are established. When the birth function is not monotone, the minimal
wave speed of nontrivial traveling wave solutions is obtained. The results are
proved by the construction of upper and lower solutions and application of the
fixed point theorem
Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System
This paper is concerned with the traveling wave solutions of an
integro-difference competition system, of which the purpose is to model the
coinvasion-coexistence process of two competitors with age structure. The
existence of nontrivial traveling wave solutions is obtained by constructing
generalized upper and lower solutions. The asymptotic and nonexistence of
traveling wave solutions are proved by combining the theory of asymptotic
spreading with the idea of contracting rectangle
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