# Advances in kinetic theory and computing : selected papers by Perthame B. (ed.)

By Perthame B. (ed.)

This paintings includes 36 brief papers on growth in quite a few topics in mathematical and theoretical physics, written for the lawsuits of a symposium in honor of the seventieth birthday of Professor F.Y. Wu, held on the Nankai Institute of arithmetic, October 7-11, 2001. the gathering of papers is geared toward researchers, together with graduate scholars, with an interdisciplinary curiosity and offers a quick creation to a few of the themes of present curiosity. those contain effects on precisely solvable versions in statistical mechanics, integrable throughout the Yang-Baxter equations, quantum teams, fractional data, random matrices, index theorems at the lattice, and different similar issues I. Vlasov-Poisson in plasma physics -- II. Quantum mechanics and semiconductors -- III. Boltzmann equations and gasoline dynamics

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Jaffard, F. A. Raviart The Child-Langmuir asymptotics of the Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric diodes: part II, Analysis of the reduced problem and determination of the Child-Langmuir current, internal report 9313 CMLA, ENS de Cachan submitted to SIAM Appl. Math. [12] P. Degond and F Poupaud, The multidimensional Child-Langmuir problem in the kinetic theory of charged-particles, (in preparation). [13| P. Degond, F. Poupaud and C. Schmeiser, A mathematical analysis of a multidimensional Schottky diode problem, (in preparation).

On the other hand, the fact that a shift can be expressed in the corresponding Fourier space - by simply changing the phase - suggests the use o f Fast Fourier Transform (FFT). 1/ Fourier in v interpolation method: Let us recall briefly the main features o f the Fourier in x/ Fourier in v interpolation method. By performing a Fourier transform in the x space (* being the conjugated position variable). Eq. 11) while a Fourier transform in the V space (X being now the conjugate o f the velocity space variable) applied to Eq.

On Math. Anal. [3] N . Ben Abdallah and P. Degond, On the Child-Langmuir taw for semiconductors. Proceedings of the Institute of Mathematics and its Applications, Minneapolis, to appear. (4) N . Ben Abdallah and P. Degond, The Child-Langmuir law for the Boltzmann Equation of Semiconductors, preprint, to appear in SIAM J. on Math. Anal. [5] N . Ben Abdallah and P. Degond, The Child-Langmuir law in the kinetic tkeory of charged-particles; Part 2, magnetised flows, plasmas and numerical algorithms, (in preparation).