場所　203教室（神戸三田キャンパス理工学部4号館2階）
今回は２件の講演です．

講演題目　「Theoretical and Numerical Analysis for an Adsorbate-Induced Phase Transition Model」
講演者　青木 崇明（関西学院大学大学院理工学研究科数理科学専攻 D1）
日時　2015年8月11日（火）10:00-10:30
講演内容

Hildebrand, Ipsen, Mikhailov and Ertl (New J. Phys. 5 (2003)) proposed an adsorbate-induced phase transition model. Takei and Yagi (Sci. Math. Jpn. 61 (2005)) showed numerically that various spatio-temporal patterns emerged in the model. Kuto and Tsujikawa (RIMS Kokyuroku Bessatsu B3 (2007)) also proved the existence of nontrivial solutions to the model, which bifurcated from a unique uniform state by using the local bifurcation theory. In this study, we find stationary patterns numerically corresponding to the bifurcated nontrivial solutions and show the stability of the evoluting solutions.

講演題目　「Numerical Computations for Growing Crystal Surface Model Under Dirichlet Conditions」
講演者　Somayyeh Azizi（大阪大学大学院工学研究科応用物理学専攻 D3）
日時　2015年8月11日（水）10:30-11:30
講演内容

In this study we consider the initial boundary value problem for a nonlinear parabolic equation of forth order in a two–dimensional bounded domain. The equation was presented by Johnson, Orme, Hunt, Graff, Sudijono, Sauder and Orr (Phys. Rev. Lett. 72(1994)), in order to describe the process growing of crystal surface by mathematical model under Dirichlet boundary condition. In this talk, we will present numerical simulation results in an interval and rectangular domains. This shows that: with the time increases a numerical solution converges to a stationary solution. When the surface roughening coefficient ¥mu is sufficiently small, a unique homogeneous stationary solution u=0 is stable because surface diffusion is stronger than roughening. When ¥mu is sufficiently large, u=0 is unstable because roughening is stronger than surface diffusion, and the structure of solution changes to a hills pattern. With increasing ¥mu the number of hills increases.