Solution to the triharmonic heat equation.
Solutions à près de systèmes d’équations aux dérivées partielles non linéaires de type mixte posés sur des ouverts non bornés
La résolution d’un système d’EDP non linéaires, de type mixte et sous contraintes, est étudiée dans des ouverts non bornés. Le cas considéré est celui d’un modèle d’écoulement transsonique avec condition d’entropie. Le problème est ramené à l’annulation d’une fonctionnelle positive pénalisée, dans un cadre hilbertien. Des solutions généralisées à près sont obtenues par encadrement de la borne inférieure de la fonctionnelle. Si les contraintes sont omises et sous certaines hypothèses, un algorithme...
Solutions analytiques des équations aux dérivées partielles à coefficients constants
Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique
Solutions fondamentales exactes
Exact fundamental solutions are known for operators of various types. We indicate a general approach that gives various old and new fundamental solutions for operators with double characteristics. The solutions allow one to read off detailed behavior, such as the presence or absence of analytic hypoellipticity. Recent results for operators with multiple characteristics are also described.
Solutions globales des équations d’Einstein-Maxwell
En adaptant une méthode de Lindblad et Rodnianski, on prouve l’existence de solutions globales pour les équations d’Einstein-Maxwell en dimension d’espace . Les données initiales considérées sont lisses, asymptotiquement euclidiennes et suffisamment petites. On utilise la jauge harmonique et la jauge de Lorenz.
Solutions of boundary-value problems in discretized volumes.
Solutions of the equation
Solutions of type for a class of singular equations.
Solutions to elliptic systems of Hamiltonian type in .
Solutions to integro-differential parabolic problems arising in the pricing of financial options in a Lev́y market.
Solutions to time-fractional diffusion-wave equation in cylindrical coordinates.
Solutions which are flat or Singular on Totally Characteristic Manifolds of first order Partial Differential Equations
Solvability for a class of non-homogeneous differential operators on two-step nilpotent groups.
Solvability of invariant sublaplacians on spheres and group contractions
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
Solving heat and wave-like equations using He's polynomials.
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...
Some aspects of holomorphic approximations from the point of view of PDEs
Some asymptotic error estimates for finite element approximation of minimal surfaces