Passage to the limit over small parameters in the viscous Cahn–Hilliard equation☆
Passage to the limit over small parameters in the viscous Cahn–Hilliard equation☆
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粘性 Cahn-Hilliard 方程中小参数的极限☆
DOI：
10.1016/j.jmaa.2014.06.036
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发表时间：
2014
影响因子：
1.3
通讯作者：
A. Tesei
中科院分区：
文献类型：
--
作者：
Bui Le Trong Thanh;Flavia Smarrazzo;A. Tesei
研究了粘性Cahn-Hilliard方程在非线性项φ的弱增长假设下，在不同的小参数下的奇异到极限的过程.一个严格的证明收敛到解决方案的Cahn-Hilliard方程，或Allen-Cahn方程，或Sobolev方程，取决于参数的选择，提供。我们还研究了Cahn-Hilliard方程当四阶项中的参数趋于零时的奇异极限。特别地，我们证明了极限不适定问题的Radon测度解的出现依赖于非线性项φ在无穷远处的行为.
We study singular passage to the limit over different small parameters for the viscous Cahn–Hilliard equation under weak growth assumptions on the nonlinearityφ. A rigorous proof of convergence to solutions of either the Cahn–Hilliard equation, or of the Allen–Cahn equation, or of the Sobolev equation, depending on the choice of the parameter, is provided. We also study the singular limit of the Cahn–Hilliard equation as the parameter in the fourth-order term goes to zero. In particular, we show that aRadon measure-valued solutionof the limiting ill-posed problem can arise, depending on the behavior of the nonlinearityφat infinity.