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In this paper we prove global existence for solutions of the Vlasov-Poisson system in convex bounded domains with specular boundary conditions and with a prescribed outward electrical field at the boundary.

We present an asymptotic analysis of the Gunn effect in a drift-diffusion model—including electric-field-dependent generation-recombination processes—for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and… (More)

Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric coefficients and chemical kinetics and whether or not diffusion is taken into account. This paper studies the… (More)

In this paper we prove the existence of a large class of periodic solutions of the Vlasov-Poisson in one space dimension that decay exponentially as t → ∞. The exponential decay is well known for the linearized version of the Landau damping problem. The results in this paper provide the first example of solutions of the whole nonlinear Vlasov-Poisson system… (More)

In this paper a one-dimensional Keller-Segel model with a logarithmic chemotactic-sensitivity and a non-diffusing chemical is classified with respect to its long time behavior. The strength of production of the non-diffusive chemical has a strong influence on the qualitative behavior of the system concerning existence of global solutions or Dirac-mass… (More)

In this paper we describe the fundamental solution of the equation that is obtained linearizing the Uehling-Uhlenbeck equation around the steady state of Kolmogorov type f (k) = k −7/6. Detailed estimates on its asymptotics are obtained.

1 Formulation of the problem In this paper we consider a quasi-stationary model of crack propagation in a two-dimensional elastic medium occupying a bounded domain. The model, developed in [3], is based on earlier work [1], [4], [9], [10], [11]. The motion of the tip X(t) of the crack k (t) at time t is given by _ X(t) = (j _ X (t) j) J (X (t)) (1.1) where… (More)

The Vlasov-Poisson system describes interacting systems of collision-less particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like t −3 at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so… (More)