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第 201 回 Q-NA セミナー #include(QNA201,notitle) 日時 : 2007 年 4月 10日(火曜) 15:30 - 17:00 場所 : 九州大学箱崎キャンパス 理学部 3号館 3階 3311 号室 講演者 : [[Pedro Lima>http://www.math.ist.utl.pt/professor.phtml.pt?who=plima]] (Instituto Superior Tecnico, Lisboa, Portugal) 題目 : Numerical and Asymptotic Analysis of Nonlinear Boundary Value Problems with Bubble-type Solutions 講演概要:~ In this talk we are concerned about singular boundary value problems arising in hydrodynamics and cosmology. In the case of spherical simmetry, the orginal partial differential equation may be reduced to a second order ordinary differential equation (ODE). This is the case, for example, of the formation of bubbles or droplets in a mixture gas-liquid. We are interested on solutions of the resulting ODE which are strictly increasing on the positive semi-axis and have finite limits at 0 and ∞ (bubble-type solutions). Necessary and sufficient conditions for the existence of such solutions are obtained in the form of a restriction on the equation coefficients. The asymptotic behavior of certain solutions of this equation is analysed near the two singularities (when r→0+ and r→∞), where the considered boundary conditions define one-parameter families of solutions. Based on the analytic study, an efficient numerical method is proposed to compute approximately the needed solutions of the above problem. Some results of the numerical experiments are displayed and their physical interpretation is discussed.
