Juan J. L. Velázquez

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We present an asymptotic analysis of the Gunn effect in a driftdiffusion 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 annihilation(More)
In this paper, we use singular perturbation methods to study the structure of travelling waves for some reaction-diffusion models obtained from the Martiel-Goldbeter and Goldbeter-Segel's models of cAMP signalling in Dictyostelium discoideum. As a consequence, we derive analytic formulae for quantities like wave speed, maximum concentration and other(More)
In this paper we propose a mechanism for the formation of paths of minimal length between two points (trails) by a collection of individuals undergoing reinforced random walks. This is the case, for instance, of ant colonies in search for food and the development of ant trails connecting nest and food source. Our mechanism involves two main ingredients: (1)(More)
f (0, x, v) = f0 (x, v) x ∈ Ω , v ∈ R (1.4) f (t, x, v) = f (t, x, v∗) x ∈ Ω , v ∈ R , t > 0 (1.5) where Ω is a convex bounded domain with C5 boundary, nx denotes the outer normal to ∂Ω and (1.6) f0 (x, v) ≥ 0 Here f (t, x, v) denotes the distribution density of electrons, φ (t, x) is the electric potential. The function h in (1.3) will be assumed to be(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 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)
We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different(More)