Sur les solutions fondamentales d'ordre fini de croissance.
Sur quelques problèmes à frontière libre analytique dans le plan
Sur un problème à frontière libre de la physique des plasmas
Ce papier porte sur l’étude mathématique d’une équation du type de Grad-Mercier qui décrit, dans certaines circonstances, l’équilibre d’un plasma confiné [H. Grad, P.N. Hu et D.C. Stevens, Proc. Nat. Acad. Sci. USA, 72,n10 (1975), 3789–3793, C. Mercier, Publication of Euratom, CEA, Luxembourg (1974), C. Mercier, Communications personnelles à R. Temam et aux auteurs]. Il s’agit de trouver une fonction “régulière” solution du systèmeoù est un ouvert borné régulier de , etL’opérateur non linéaire...
Sur un système d'inégalités différentielles partielles du second ordre à argument fonctionnel
Sur une équation différentielle abstraite à domaine variable; applications aux problèmes mixtes, du type Cauchy-mêlé, pour l'équation de la chaleur
Surface temperature determination from borehole measurements: Regularization and error estimates.
Symmetry theorems and uniform rectifiability.
Système d'inégalités aux différences finies du type elliptique
Systems for phase transitions with hysteresis effect
Systems of degenerate differential equations in Banach spaces.
Systems of quasilinear parabolic equations with discontinuous coefficients and continuous delays.
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.
The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries
We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.
The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations
In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence,...
The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations
In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence, and convergence properties, of this algorithm. We...
The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations
In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence,...
The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations
The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations
This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of...
The Becker-Döring model with diffusion. I. Basic properties of solutions
The behavior of the free boundary for the dam problem