Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains
Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals.
Study of a three component Cahn-Hilliard flow model
In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations.
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.
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...
Sur la méthode des différences finies pour un système d'équations différentielles non linéaires paraboliques sans dérivées mixtes avec une condition aux limites du type de Neumann
Sur l'approximation des équations de Schrödinger non-linéaires par une méthode de décomposition
Sur l'existence et la régularité des solutions faibles d'une inéquation parabolique non linéaire.
Sur l'existence et unicité de solutions d'un modèle approximé des équations d'évolution tridimensionnelles d'un cristal liquide nématique
Sur une classe de problèmes d'évolution non linéaires et dégénérés
Sur une équation d'évolution non linéaire liée à la théorie de la turbulence
Sur une famille biparamétrique de schémas des différences finies pour un système d'équations paraboliques aux dérivées mixtes et avec des conditions aux limites du type de Neumann
Sur une méthode des différences finies pour une équation non linéaire différentielle fonctionnelle aux dérivées mixtes
Sur un'équation d'évolution multivoque et non monotone dans un espace de Hilbert
Sur un'inéquation parabolique dans un ouvert non cylindrique
Symmetrization in nonlinear parabolic equations
Symmetry and geometric evolution equations.