-estimates for the Cauchy-Riemann equations on certain weakly pseudoconvex domains
Calcul de Weyl et opérateurs sous elliptiques
Calcul des singularités par la méthode des éléments finis
Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II
Soit un opérateur pseudodifférentiel (ou microdifférentiel) tel que soit aussi un opérateur pseudodifférentiel. Alors le symbole de s’ecrit avec un symbole . Pour la réciproque, si est un opérateur à symbole , il existe un opérateur tel que . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.
Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
Cet article s’intéresse au calcul symbolique des opérateurs microdifférentiels avec symboles exponentiels. On donne la loi de composition des symboles exponentiels. Comme application, on trouve une condition suffisante d’ellipticité pour les opérateurs microdifférentiels d’ordre infini.
Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
Calcul symbolique et singularités des solutions des équations aux dérivées partielles non linéaires
Cascade of phases in turbulent flows
This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.
Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients
In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.
Cauchy problem for the complex Ginzburg-Landau type Equation with -initial data
This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation in with -initial data in the subcritical case (), where is a complex-valued unknown function, , , , , , , and . The proof is based on the - estimates of the linear semigroup and usual fixed-point argument.
Cauchy problems with periodic controls.
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Cauchy-Kowalewski theorems in Clifford analysis : a survey
Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative
2000 Mathematics Subject Classification: 35A15, 44A15, 26A33The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
Characterization of the solutions of a 2b-parabolic operator with initial data in BMO
Chirps -dimensionnels et analyse -microlocale
Classical Solutions of the Chain Equations.
Classification of differential invariant submodels.
Classification of Monge-Ampère equations with two variables
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.