Remarques sur des résultats d'existence pour les équations de Hamilton-Jacobi du premier ordre
Renormalized entropy solutions of scalar conservation laws
Résurgence d'un thème de Huygens-Fresnel
Schwarz-sche Randwertaufgabe fur eine Klasse der verallgemeinerten analytischen Funktionen
Sharp Domains of Determinacy and Hamilton-Jacobi Equations
If is a linear hyperbolic system of partial differential operators for which local uniqueness in the Cauchy problem at spacelike hypersurfaces is known, we find nearly optimal domains of determinacy of open sets . The frozen constant coefficient operators determine local convex propagation cones, . Influence curves are curves whose tangent always lies in these cones. We prove that the set of points which cannot be reached by influence curves beginning in the exterior of is a domain of...
Singular dynamics for semiconcave functions
Singularly perturbed set of periodic functional-differential equations arising in optimal control theory
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
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 de viscosité des équations de Hamilton-Jacobi du premier ordre et applications
Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique
Solutions indéfiniment différentiables d’un système d’équations aux différences et application aux systèmes d’équations aux dérivées partielles
Dans cette note, nous prouvons l’existence de solutions indéfiniment différentiables d’un système de deux équations aux différences et appliquons la technique utilisée à l’étude des systèmes d’équations linéaires aux dérivées partielles.Dans chaque cas, on montre que les solutions sont les premières composantes des solutions d’un système matriciel que nous étudions.
Solutions of Analytical Systems of Partial Differential Equations
In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).
Solutions of DEs and PDEs as potential maps using first order Lagrangians.
Solutions of the equation
Solutions to the equation div u = f in weighted Sobolev spaces
We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces , where the weight function w is in the class of Muckenhoupt weights .
Solutions which are flat or Singular on Totally Characteristic Manifolds of first order Partial Differential Equations
Soluzioni di viscosità
This is the expanded text of a lecture about viscosity solutions of degenerate elliptic equations delivered at the XVI Congresso UMI. The aim of the paper is to review some fundamental results of the theory as developed in the last twenty years and to point out some of its recent developments and applications.
Solvability near the characteristic set for a class of planar vector fields of infinite type
We study the solvability of equations associated with a complex vector field in with or coefficients. We assume that is elliptic everywhere except on a simple and closed curve . We assume that, on , is of infinite type and that vanishes to a constant order. The equations considered are of the form , with satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of is , the equation is solvable in the category but not in the category....
Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods
This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem...
Some aspects of holomorphic approximations from the point of view of PDEs