Indépendance des fréquences par rapport aux solutions quasi- periodiques de certaines équations d'evolution non linéaires.
Inhomogeneous parabolic Neumann problems
Second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions are studied. Existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder are proved using methods from the theory of integrated semigroups, showing in particular the well-posedness of the abstract Cauchy problem in spaces of continuous functions. Under natural assumptions on the coefficients and the inhomogeneity the...
Intégrabilité d'une classe de systèmes de lois de conservation.
Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics
We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...