Some isometrical identities in the wave equation.
Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some new results in multiphase geometrical optics
Some new results in multiphase geometrical optics
In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...
Some nonexistence results for higher-order evolution inequalities in cone-like domains.
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.