Large time behaviour of the solutions to some nonlinear evolution equations
Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace
L’existence d’une solution classique d’une éqéaire dans (Communication préalable)
Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions
We study one-dimensional linear hyperbolic systems with -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.
Liouville type results for periodic and almost periodic linear operators
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation . We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.
Lyapunov center theorem for some nonlinear PDE's : a simple proof