接触线动力学演化中的瞬时奇异性
Finite-time singularities in the dynamical evolution of contact lines
摘要：
研究半无限直线上变速线性平流-扩散方程的有限时间奇性。可变速度由边界处的附加条件确定，该附加条件模拟了180 °接触角下的流体动力学流的接触线的动力学。使用先验能量估计，我们得到的条件，变速，保证充分光滑的线性对流-扩散方程的解决方案，在有限的时间内爆炸。利用线性对流-扩散方程的自相似解类，我们得到了奇异性形成的爆破速率。这个爆破率不同意与以前的数值模拟的模型问题。
英文摘要：
We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact angle. Using apriori energy estimates, we derive conditions on variable speed that guarantee that a sufficiently smooth solution of the linear advection--diffusion equation blows up in a finite time. Using the class of self-similar solutions to the linear advection-diffusion equation, we find the blow-up rate of singularity formation. This blow-up rate does not agree with previous numerical simulations of the model problem.
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