Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations.
Sul modulo di continuità alla frontiera della soluzione del problema di Dirichlet relativo ad una classe di operatori parabolici
Sul problema di Cauchy per le equazioni paraboliche astratte di ordine
Sul problema di Cauchy-Dirichlet per una classe di operatori parabolici a coefficienti discontinui
Sul problema di Cauchy-Neumann per le equazioni paraboliche singolari a coefficienti discontinue in due variabili
Sulla diffusione del calore in un conduttore irradiato
Sulle equazioni differenziali astratte degeneri
Sulle equazioni paraboliche semilineari di ordine arbitrario in uno spazio di Banach
Summability of semicontinuous supersolutions to a quasilinear parabolic equation
We study the so-called -superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when , we have supercaloric functions and the heat equation. We show that the -superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.
Summability of the solutions to nonlinear parabolic equations with measure data.
Summation of polyparametrical functional series by the method of finite hybrid integral transforms (Fourier, Bessel)
Super and ultracontractive bounds for doubly nonlinear evolution equations.
We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = Δp(um) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q ≤ C||u0||rγ / tβ for any r ≤ q ∈ [1,+∞) and t > 0 and...
Superconvergence of finite element method for parabolic problem.
Superconvergence of mixed finite element methods for parabolic equations
Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u), Part II.
In this paper we consider a nonlinear parabolic equation of the following type:(P) ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u)with Dirichlet boundary conditions and initial data in the case when 1 < p < 2.We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with (P).
Supersolutions and stabilization on the solution of a nonlinear parabolic system.
Support re-splitting phenomena caused by an interaction between diffusion and absorption
Sur des problèmes d’asservissements stratigraphiques
On expose les difficultés d’ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l’Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d’unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d’un problème inverse posé par l’étude stratigraphique d’une colonne monolithologique.
Sur des problèmes d'asservissements stratigraphiques
On expose les difficultés d'ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l'Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d'unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d'un problème inverse posé par l'étude stratigraphique d'une colonne monolithologique.
Sur deux théorèmes curieux signalés par M. Poincaré