Neumann operator for wave equation in a half space and microlocal orders of singularities along the boundary
New singular solutions of Protter's problem for the 3D wave equation.
Nonclassical problems for the second order hyperbolic equations.
Non-existence results for a semilinear hyperbolic problem with boundary condition of memory type.
Nonhomogeneous boundary value problem for a semilinear hyperbolic equation
We discuss the solvability of a nonhomogeneous boundary value problem for the semilinear equation of the vibrating string in a bounded domain and with a certain type of superlinear nonlinearity. To this end we derive a new dual variational method.
Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions.
Nonlinear transmission problem with a dissipative boundary condition of memory type.
Nonlinear vibrations of completely resonant wave equations
We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
Null form estimates for symbols and local existence for a quasilinear dirichlet-wave equation
Numerical controllability of the wave equation through primal methods and Carleman estimates
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null...
Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets
A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...
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.