Anomalous Exponents and Dipole Solutions for the Thin Film Equation
Anomalous Exponents and Dipole Solutions for the Thin Film Equation
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薄膜方程的反常指数和偶极子解
DOI：
10.1137/s0036139900366936
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Bowen
中科院分区：
文献类型：
--
作者：
J. Hulshof;J. King;M. Bowen
我们研究了“薄膜”方程的相似解。特别是，我们看看解决方案的半线$x\ge0$与紧凑的支持和零接触角的边界条件在x=0。这种“偶极”解具有反常指数，因此称为第二类相似解。使用相空间分析和数值模拟相结合，我们在数值上构建代表这些解决方案的轨迹，在同一时间获得更广泛的洞察四维相空间的性质。额外的渐近分析提供了关于演化到自相似性的进一步信息。
We investigate similarity solutions of the "thin film" equation. In particular we look at solutions on the half-line $x\ge0$ with compact support and zero contact angle boundary conditions in x=0. Such "dipole" solutions feature an anomalous exponent and are therefore called similarity solutions of the second kind. Using a combination of phase space analysis and numerical simulations, we numerically construct trajectories representing these solutions, at the same time obtaining broader insight into the nature of the four-dimensional phase space. Additional asymptotic analysis provides further information concerning the evolution to self-similarity.