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DCDS-B

There exists a large family of water waves with jump discontinuities in the vorticity.
These waves travel at a constant speed.
They are two-dimensional, periodic, symmetric, and subject to the influence of gravity.
Some of them have large amplitudes.
Their existence is proven using local and global bifurcation theory, together with
elliptic theory of weak solutions with nonlinear boundary conditions.

DCDS

Consider a nonlinear wave equation in three space dimensions with zero
mass together with a negative potential. If the potential is sufficiently short-range,
then it does not alter the global existence of small-amplitude solutions. On the other
hand, if the potential is sufficiently large, it will force some solutions to blow up in
a finite time.

DCDS

We present a new and simpler proof that the nonlinear scattering operator $\S$ is analytic on energy space.
We apply it in particular to a fourth-order nonlinear wave equation in R

^{n}. In addition, we prove that $\S$ determines the scatterer uniquely and that for small powers there is no scattering.
DCDS

We study the Vlasov-Poisson-Fokker-Planck system. For arbitrary data we
prove the global well-posedness and gain of regularity of solutions under improved assumptions.
We also prove that if the initial data are sufficiently small, the solutions satisfy
optimal rates of asymptotic decay.

DCDS

Consider a propagator defined on a Banach space whose norm satisfies an
appropriate exponential bound. To this operator is added a bounded operator which is
relatively smoothing in the sense of Vidav. The location of the essential spectrum of the
perturbed propagator is then estimated. An application to kinetic theory is given for a
system of particles that interact both through collisions and through their charges.

keywords:
rare
gases
,
stability
,
Vlasov–Poisson–Boltzmann System
,
plasmas
,
perturbation of propagators
,
spectral theory.

KRM

N/A

KRM

We establish the global-in-time existence and uniqueness of classical solutions
to the ``one and one-half'' dimensional
relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is
infinitely large at the spatial boundary. We prove that
the large external magnetic field confines the particles to a compact set away from the boundary.
This excludes the known singularities that typically occur due to particles that repeatedly bounce off the boundary.
In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer,
who studied the Cauchy problem without boundaries.

## Year of publication

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