119 research outputs found
Fichier matières "noms de personnes " de la Bibliothèque administrative de la Préfecture de la Seine (Le)
Sharp large time behaviour in -dimensional reaction-diffusion equations of bistable type
We study the large time behaviour of the reaction-diffsuion equation
in spatial dimension , when the nonlinear term
is bistable and the initial datum is compactly supported. We prove the
existence of a Lipschitz function of the unit sphere, such that
converges uniformly in , as goes to infinity, to
, where is the unique 1D
travelling profile. This extends earlier results that identified the locations
of the level sets of the solutions with precision, or
identified precisely the level sets locations for almost radial initial data
Global Existence and Long-Time Asymptotics for Rotating Fluids in a 3D Layer
The Navier-Stokes-Coriolis system is a simple model for rotating fluids,
which allows to study the influence of the Coriolis force on the dynamics of
three-dimensional flows. In this paper, we consider the NSC system in an
infinite three-dimensional layer delimited by two horizontal planes, with
periodic boundary conditions in the vertical direction. If the angular velocity
parameter is sufficiently large, depending on the initial data, we prove the
existence of global, infinite-energy solutions with nonzero circulation number.
We also show that these solutions converge toward two-dimensional Lamb-Oseen
vortices as time goes to infinity.Comment: 26 pages, no figur
Sharp large time behaviour in n-dimensional Fisher-KPP equations
We study the large time behaviour of the Fisher-KPP equation ∂tu = ∆u+u−u2 in spatial dimension N, when the initial datum is compactly supported. We prove the existence of a Lipschitz function s∞ of the unit sphere, such that u(t, x) approaches, as t goes to infinity, the function Uc∗ ( |x| − c∗t + Nc+∗2 lnt + s∞(|xx| )) , where Uc∗ is the 1D travelling front with minimal speed c∗ = 2. This extends an earlier result of Gärtner
Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
We construct travelling wave graphs of the form , , , solutions to the
-dimensional forced mean curvature motion ()
with prescribed asymptotics. For any 1-homogeneous function ,
viscosity solution to the eikonal equation
, we exhibit a smooth concave solution to
the forced mean curvature motion whose asymptotics is driven by
. We also describe in terms of a probability
measure on .Comment: 36 pages, 6 figure
A primeira partilha da África: decadência e ressurgência do comércio português na Costa do Ouro (ca. 1637-ca. 1700)
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