The limiting equation for Neumann Laplacians on shrinking domains.
The Picard-Ionescu problem for hyperbolic inclusions with modified argument
We consider the Picard-Ionescu problem for hyperbolic inclusions with modified argument. Existence of a local solution is proved and some properties of the set of solutions are established.
The pseudo--Laplace eigenvalue problem and viscosity solutions as
We consider the pseudo--laplacian, an anisotropic version of the -laplacian operator for . We study relevant properties of its first eigenfunction for finite and the limit problem as .
The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → ∞
We consider the pseudo-p-Laplacian, an anisotropic version of the p-Laplacian operator for . We study relevant properties of its first eigenfunction for finite p and the limit problem as p → ∞.
The regularized asymptotics in the singularly perturbed parabolic problem with angular boundary layers.
The second eigenvalue of the -Laplacian as goes to 1.
The speed of propagation for KPP type problems. I: Periodic framework
This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
The Tartar equation for homogenization of a model of the dynamics of fine-dispersion mixtures.
The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation
We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications...
The Wiener criterion and quasilinear uniformly elliptic equations
Topological properties of the solution set of a class of nonlinear evolutions inclusions
In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field , we are able to show that the solution set is in fact an -set. Finally some applications to infinite dimensional control systems are also presented.
Traces and the F. and M. Riesz theorem for vector fields
This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field . Applications to the F. and M. Riesz property for vector fields are discussed.
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.
Un résultat générique d’unicité pour les équations d’évolution
Soit un espace topologique, un espace métrique et un système d’équations d’évolution admettant une solution dans pour toute donnée initiale dans et stable vis-à-vis des données initiales sur . On montre que l’ensemble des données initiales pour lesquelles admet une unique solution est un de . En particulier, si l’unicité est vraie sur un sous-ensemble dense de , elle l’est génériquement.
Una classe di soluzioni asintotiche per una equazione ellittica degenere
Unicité pour le problème de Cauchy à partir d'une surface partout caractéristique ; applications
Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition
Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.
Uniqueness of global positive solution branches of nonlinear elliptic problems.
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains