General method of integration of partial differential equations of the n-th order
General solutions of certain nonlinear partial differential equations
Geometry of the Complex Homogeneous Monge-Ampère Equation.
Higher integrability for weak solutions of higher order degenerate parabolic systems.
Hypoellipticité d'équations aux dérivées partielles non linéaires
Integrable hierarchy of higher nonlinear Schrödinger type equations.
Interior estimates for solutions of Abreu's equation.
This paper develops various estimates for solutions of a nonlinear, fouth order PDE which corresponds to prescribing the scalar curvature of a toric Kähler metric. The results combine techniques from Riemannian geometry and from the theory of Monge-Ampère equations.
Isothermic surfaces as solutions of Calapso PDE.
Le problème d’équivalence locale pour un système scalaire complet d’équations aux dérivées partielles d’ordre deux à variables indépendantes
Dans le présent article, nous établissons une caractérisation des systèmes scalaires d’équations aux dérivées partielles analytiques d’ordre deux à variables indépendantes équivalents par un changement de coordonnées analytique au système , .
Les équations de Monge-Ampère homogènes, et des exhaustions spéciales de variétés affines
Les propriétés asymptotiques des solutions d’une équation différentielle nonlinéaire d’ordre
Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations
Method of Rothe in evolution equations
Multiplicity and structures for traveling wave solutions of the Kuramoto-Sivashinsky equation.
Nonlinear Evolution Equations and Analyticity. I
Nouvelles estimations pour les solutions d'équations aux dérivées partielles non linéaires
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Observations on quasi-linear partial differential equations
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.