Browsing Mathematics (Faculty of) by Author "Aoki, Yasunori"
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Analysis of Asymptotic Solutions for Cusp Problems in Capillarity
Aoki, Yasunori (University of Waterloo, 2007-09-27)The capillary surface $u(x,y)$ near a cusp region satisfies the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=&\kappa u \qquad \textrm{in }\left\{(x,y): ... -
Study of Singular Capillary Surfaces and Development of the Cluster Newton Method
Aoki, Yasunori (University of Waterloo, 2012-08-29)In this thesis, we explore two important aspects of study of differential equations: analytical and computational aspects. We first consider a partial differential equation model for a static liquid surface (capillary ...