A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model.
A semilinear parabolic boundary-value problem in bioreactors theory.
A singular radially symmetric problem in electrolytes theory
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
A smoothing property for the -critical NLS equations and an application to blowup theory
A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom.
A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations
A system of nonlinear degenerate parabolic equations.
A theorem of Rolewicz's type for measurable evolution families in Banach spaces.
A variational approach in weighted Sobolev spaces to the operator - ... + .../... X1 in exterior domains of IR3.
A variational approach to the local character of -closure : the convex case
A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions.
A wave equation with discontinuous time delay.
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution of an elliptic equation, that we write , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to...
About global existence and asymptotic behavior for two dimensional gravity water waves
The main result of this talk is a global existence theorem for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds.The proof is based on a bootstrap argument involving and estimates. The bounds are proved in the paper [5]. They rely on a normal forms paradifferential method allowing one to obtain energy estimates on the Eulerian formulation...
About steady transport equation. II: Schauder estimates in domains with smooth boundaries.
Abstract linear hyperbolic equations and asymptotic equivalence as
Abstract parabolic problem with non-Lipschitz nonlinearity
An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
Abstract parabolic problems in ordered Banach spaces
We consider abstract parabolic problems in ordered Banach spaces and give conditions under which they have global attractors. Our approach is via comparison of solutions. Within this approach abstract comparison principles are obtained and bounds on the attractors are given by order intervals in Banach spaces. These results are applied to ordinary differential equations and to parabolic equations for which the main part is given by a sum of fractional powers of sectorial operators having increasing...
Adaptive stabilization of continuous-time systems through a controllable modified estimation model.
Adiabatic approximation for a two-level atom in a light beam
Following the recent experimental realization of synthetic gauge potentials, Jean Dalibard addressed the question whether the adiabatic ansatz could be mathematically justified for a model of an atom in 2 internal states, shone by a quasi resonant laser beam. In this paper, we derive rigorously the asymptotic model guessed by the physicists, and show that this asymptotic analysis contains the information about the presence of vortices. Surprisingly, the main difficulties do not come from the nonlinear...