Quelques propriétés de solutions d'équations et d'inéquations d'évolution paraboliques non linéaires
Caractérisation d'un espace fonctionnel intervenant en contrôle optimal
Régularité de la solution d'un problème aux limites non linéaires
Extension of distributions and representation by derivatives of continuous functions.
It is proved that any Banach valued distribution on a bounded set can be extended to all of if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued distribution...
Non linear representations of Lie groups
Existence of semi-periodic solutions of steady Navier-Stokes equations in a half space with an exponential decay at infinity
Modelling of convective phenomena in forest fire.
We present a model coupling the fire propagation equations in a bidimensional domain representing the surface, and the air movement equations in a three dimensional domain representing an air layer. As the air layer thickness is small compared with its length, an asymptotic analysis gives a three dimensional convective model governed by a bidimensional equation verified by a stream function. We also present the numerical simulations of these equations.
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