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The aim of this work is to introduce and to analyze new algorithms for solving the
transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be,
on the one hand faster than some classic algorithms and easily to be implemented and naturally
deviced for parallelisation on the other hand. They are based on a splitting of the collision operator
holding amount of caracteristics of the transport operator. Some numerical results are given at the end
of this work.
...
In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval with a tolerance level . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant....
The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.
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