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Some decay problems of a collisionless gas: Numerical study

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Partial Differential Equations in Kinetic Theories

We investigate time-dependent behavior of a collisionless (or highly rarefied) gas in the following two problems:

(i) A collisionless gas is confined in a closed domain bounded by a diffusely reflecting wall with a uniform temperature. The approach of the gas to an equilibrium state at rest, caused by the interaction of gas molecules with the wall, is investigated numerically. It is shown that the approach is slow and proportional to an inverse power of time. This is a joint work with T. Tsuji and F. Golse.

(ii) An infinite plate without thickness is placed in a collisionless gas, and an external force, obeying Hooke’s law, is acting perpendicularly on the plate. If the plate is displaced perpendicularly from its equilibrium position and released, then it starts an oscillatory motion, which decays as time goes on because of the drag exerted by the gas molecules. This unsteady motion is investigated numerically, under the diffuse reflection condition, with special interest in the manner of its decay. It is shown that the decay of the displacement of the plate is slow and is in proportion to an inverse power of time. The result complements the existing mathematical study of a similar problem [S. Caprino, et al., Math. Models. Meth. Appl. Sci. 17, 1369 (2007)] in the case of non-oscillatory decay. This is a joint work with T. Tsuji.

This talk is part of the Isaac Newton Institute Seminar Series series.

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