Über die Beschränktheit der zweiten Ableitungen der Lösungen nichtlinearer elliptischer Differentialgleichungen.
Über die Existenz klassischer Lösungen semilinearer parabolischer Differentialgleichungen höherer Ordnung.
Über die Hölderstetigkeit schwacher Lösungen semilinearer elliptischer Systeme mit einseitiger Bedingung.
Über eine Koerzitivitätsgleichung in ... .
Über nichtlineare, konkave, elliptische Differentialgleichungen.
Über quasilineare elliptische Differentialgleichungen in der Ebene.
Un formalisme pour les estimations de type Kružkov pour les lois de conservation scalaires
On montre comment le formalisme introduit récemment par l’auteur et Benoît Perthame permet de justifier la plupart des estimations d’erreurs pour des solutions approchées d’une loi de conservation scalaire.
Un problema de transmisión no lineal de tipo hiperbólico-parabólico.
Une caractérisation des opérateurs elliptiques autoadjoints
Unicité du problème de Cauchy pour une classe d'opérateurs différentiels à caractéristiques de multiplicité constante
Unicité pour le problème de Cauchy à partir d'une surface partout caractéristique ; applications
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
Uniform attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
We consider the first initial boundary value problem for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The results, in particular, improve some recent ones for nonautonomous p-Laplacian equations.
Uniform boundedness and global existence of solutions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients.
Uniform estimates for a class of evolution equations
Uniform estimates for the parabolic Ginzburg–Landau equation
We consider complex-valued solutions of the Ginzburg–Landau equation on a smooth bounded simply connected domain of , , where is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of , as , is to establish uniform bounds for the gradient, for some . We review some recent techniques developed in...
Uniform estimates for the parabolic Ginzburg–Landau equation
We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of , N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...
Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.
In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equationb(u)t - div (|∇u - k(b(u))e|p-2 (∇u - k(b(u))e)) + g(x,u) = f(t,x).This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc. The solvability of this problem is established in the BVt(Q) space....
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.