Note on the inequalities of J. Kazdan.
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.
Note on the nodal line of the -Laplacian.
Note on the solution of transport equation by Tau method and Walsh functions.
Note on the stability of the Dirichlet problem and the Poisson equation
Note on the uniqueness of a global positive solution to the second Painlevé equation.
Note on two compatibility criteria: Jacobi-Mayer bracket vs. differential Gröbner basis.
Note sur l'intégration d'une certaine classe d'équations aux dérivées partielles du second ordre.
Note to periodic solvability of the boundary value problem for nonlinear heat equation
Note to the paper by R. Hempel, A. M. Hinz, and H. Kalf: On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
Notes On Partial Differential Equations III: Two Dirchlet Type Problems For Poisson's Equation
Notes on partial differential equations III: Two Dirichlet type problems for Poisson's equation.
Notes on some recent methods in bifurcation theory
Notes on symplectic non-squeezing of the KdV flow
We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korteweg-de Vries (KdV) flow on the circle . The nonsqueezing result relies on the aforementioned approximations and the finite-dimensional nonsqueezing theorem of Gromov [14]. Unlike the work of Kuksin [22] which initiated the investigation of non-squeezing results for infinite dimensional Hamiltonian systems, the nonsqueezing argument here does not construct a capacity directly. In this way our...
Nouveaux problèmes sur les équations mixtes
Nouvelle interprétation de la formule des traces de Selberg
Nouvelles estimations pour les opérateurs pseudo-différentiels
Nouvelles estimations pour les solutions d'équations aux dérivées partielles non linéaires
Nouvelles formulations intégrales pour les problèmes de diffraction d’ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....
Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all...