Problèmes paraboliques et opérateurs pseudo-différentiels
Propriétés de certaines solutions d'inégalité aux dérivées partielles de type parabolique
Quasi-geostrophic type equations with weak initial data.
Régularité de la solution forte de problèmes non linéaires d'évolution
Regularity Theorems and Optimal Errors Estimates for Linear Parabolic Cauchy Problems.
Regularized semigroups and systems of linear partial differential equations
Runge-Kutta methods for parabolic equations with nonsmooth initial data
Scattering, transformations spectrales et équations d'évolution non linéaire II
Semi-discrétisation en temps pour les équations d'évolution paraboliques lorsque l'opérateur dépend du temps
Semigroup formulation of Rothe's method: application to parabolic problems
A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe's method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Solvability of a class of phase field systems related to a sliding mode control problem
We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some remarks on time-dependent evolution systems in the hyperbolic case
Spectral analysis of long wavelength periodic waves and applications.
Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection
Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
Stability and saddle-point property for a linear autonomous functional parabolic equation
Stabilization of solutions of abstract parabolic equations
Straightening of a noncylindrical region and evolution equations