Uniform stabilization of a coupled structural acoustic system by boundary dissipation.
Uniform stabilization of a viscous numerical approximation for a locally damped wave equation
This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the mesh size)...
Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
Uniform stabilization of some damped second order evolution equations with vanishing short memory
We consider a damped abstract second order evolution equation with an additional vanishing damping of Kelvin–Voigt type. Unlike the earlier work by Zuazua and Ervedoza, we do not assume the operator defining the main damping to be bounded. First, using a constructive frequency domain method coupled with a decomposition of frequencies and the introduction of a new variable, we show that if the limit system is exponentially stable, then this evolutionary system is uniformly − with respect to the calibration...
Uniform zeros for beaded strings
Uniformly exponentially or polynomially stable approximations for second order evolution equations and some applications
In this paper, we consider the approximation of second order evolution equations. It is well known that the approximated system by finite element or finite difference is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial...
Unilateral dynamic contact of von Kármán plates with singular memory
The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem.
Unique continuation for the solutions of the laplacian plus a drift
We prove unique continuation for solutions of the inequality , a connected set contained in and is in the Morrey spaces , with and . These spaces include for (see [H], [BKRS]). If , the extra assumption of being small enough is needed.
Unique continuation theorems for solutions of partial differential equations and inequalities
Unique solvability of initial boundary-value problems for hyperbolic systems in cylinders whose base is a cusp domain.
Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.
Uniqueness in a one-dimensional problem of finding a time-dependent potential.
Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space.
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems.
Uniqueness of solutions of the Neumann problem for singular ultrahyperbolic equations
Uniqueness of the Multi-Dimensional Inverse Scattering Problem for Time Dependent Potentials.
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
Consider the energy-critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially the sum of...
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case
Following our previous paper in the radial case, we consider type II blow-up solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of concentrating at the origin.
Unstable simple modes for a class of Kirchhoff equations
Upper estimate of the interval of existence of solutions of a nonlinear Timoshenko equation.