Some non-linear s. p. d. e's that are second order in time.
Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws
We study several regularizing methods, stationary phase or averaging lemmas for instance. Depending on the regularity assumptions that are made, we show that they can either be derived one from the other or that they lead to different results. Those are applied to Scalar Conservation Laws to precise and better explain the regularity of their solutions.
Some remarks on a second order evolution equation.
Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories
Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings
Some remarks on multidimensional systems of conservation laws
This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.
Some remarks on time-dependent evolution systems in the hyperbolic case
Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type
Some results on the well-posedness for systems with time dependent coefficients
We consider hyperbolic systems with time dependent coefficients and size or . We give some sufficient conditions in order the Cauchy Problem to be well-posed in and in Gevrey spaces.
Some results on weak solutions to a class of singular hyperbolic variational inequalities
Some series whose coefficients involve the values (n) for n odd.
Some topological properties preserved by nearness between operators and applications to P.D.E.
Some uniqueness and observability problems arising in the control of vibrations
We discuss a control problem for the Lamé system which naturally leads to the following uniqueness problem: Given a bounded domain of , are there non-trivial solutions of the evolution Lamé system with homogeneous Dirichlet boundary conditions for which the first two components vanish? We show that such solutions do not exist when the domain is Lipschitz. However, in two space dimensions one can build easily polygonal domains in which there are eigenvibrations with the first component being identically...
Space adaptive finite element methods for dynamic obstacle problems.
Spatial decay estimates for a class of nonlinear damped hyperbolic equations.
Spatial problem of Darboux type for one model equation of third order.
Spectral analysis of long wavelength periodic waves and applications.
Spectral methods for numerical relativity.
Stabilisation d’une poutre. Étude du taux optimal de décroissance de l’énergie élastique
On se propose d’étudier la stabilité d’une poutre flexible homogène, encastrée à une extrémité. À l’autre extrémité est attachée une masse ponctuelle où on applique un moment proportionnel à la vitesse de déplacement angulaire. On montre par une analyse spectrale que le taux optimal de décroissance de l’énergie est déterminé par l’abscisse spectrale du générateur infinitésimal du semi-groupe associé au problème.
Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique
We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.