九州関数方程式セミナー 平成27年度前期講演

日時 6月19日(金) 16:00--17:30 【いつもと時間が異なります】
会場 福岡大学 セミナーハウス 2階 セミナー室
講師 I-Kun Chen 氏 (京都大学)
題目 On boundary singularity in kinetic theory
概要 Singular behavior near the boundary is unique in kinetic theory. We first introduce two kinds of singularity: logarithmic singularity of macroscopic variables and logarithmic singularity of the velocity distribution functions. Both of them are verified in analysis on the thermal transpiration problem. For hard sphere potential, a bootstrap strategy is applied to obtain an asymptotic formula for gradient of moments of solutions in the functional space from known existence results. The formula indicates gradient of some moments diverge logarithmically near the boundary. We further investigate the gses with cut-off hard potential. A technique of using the Holder type continuity of the integral operator to obtain integrability of the derivatives of the macroscopic variables is developed. We establish the asymptotic approximation for the gradient of the moments. Our analysis indicates the logarithmic singularity of the gradient of some moments. In particular, our theorem holds for the condensation and evaporation problems.

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