The regularized asymptotics in the singularly perturbed parabolic problem with angular boundary layers.
The relation between the porous medium and the eikonal equations in several space dimensions.
We study the relation between the porous medium equation ut = Δ(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions for the case of the Dirichlet boundary value problem.
The Riccati differential equation and a diffusion-type equation.
The role of symmetry and separation in surface evolution and curve shortening.
The second eigenvalue of the -Laplacian as goes to 1.
The shape and smoothness of stable plasma configurations
The sharp Poincaré inequality for free vector fields: an endpoint result.
The sinc-Galerkin method for solving singularly-perturbed reaction-diffusion problem.
The Singularity Expansion Method applied to the transient motions of a floating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
The Sobolev inequality on the Heisenberg group and the Yamabe problem on CR manifolds (d'après travaux avec J. M. Lee)
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 summability of solutions to variational problems since Guido Stampacchia.
Inequalities concerning the integral of |∇u|2 on the subsets where |u(x)| is greater than k can be used in order to prove regularity properties of the function u. This method was introduced by Ennio De Giorgi e Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems.
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
The Tartar equation for homogenization of a model of the dynamics of fine-dispersion mixtures.
The thermistor obstacle problem with periodic data
The topological derivative of the Dirichlet integral under formation of a thin ligament.
The Total Variation of Solutions of Parabolic Differential Equations and a Maximum Principle in Unbounded Domains.
The uniform attractors for the nonhomogeneous 2D Navier-Stokes equations in some unbounded domain.
The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation
The Vlasov equation with strong mangnetic field and oscillating electric field as a model for isotop resonant separation.