Note on the Dirichlet problem with L2-Boundary Data.
Note sur l'intégration d'une certaine classe d'équations aux dérivées partielles du second ordre.
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.
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...
Noyaux élémentaires d'équations aux dérivées partielles du premier ordre
Numerical computation of soliton dynamics for NLS equations in a driving potential.
Numerical solution of a three-dimensional integral equation
Numerical study of acoustic multiperforated plates
It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.
On a class of initial-boundary value problems in a domain with boundary containing isolated points
On a class of mixed boundary value problems for linear hyperbolic 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.
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.
On a functional differential equation arising in the theory of the distribution of wealth.
On a nonlocal Ostrovsky-Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability.
On a shock problem involving a nonlinear viscoelastic bar.
On a Volterra Stieltjes integral equation.
On a Whitham-type equation.
On an equation with partial derivations in four-dimensional Euclidean space.