Radial solutions of a class of iterated partial differential equations
We give some expansion formulas and the Kelvin principle for solutions of a class of iterated equations of elliptic type
Real and complex fundamental solutions. A way for unifying mathematical analysis.
Reflectionless boundary propagation formulas for partial wave solutions to the wave equation.
Remarques sur l'homogénéisation de certains problèmes quasi-linéaires
Remarques sur l'optique géométrique non linéaire multidimensionnelle
Representation of equilibrium solutions to the table problem of growing sandpiles
In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...
Representation of Green's function for the Dirichlet problem of polyharmonic equations in a ball.
Representation theorem for the solution of weakly hyperbolic equations with fast oscillating coefficients
Representation theorems and Fatou theorems for parabolic systems in the sense of Petrovskiĭ
Reproducing kernel methods for solving linear initial-boundary-value problems.
Resolvent kernel for the Kohn Laplacian on Heisenberg groups.
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
Root systems and hypergeometric functions. I
Root systems and hypergeometric functions. II