Juan J. L. Velázquez

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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)
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)
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)