论文标题
在具有P-Laplacian的广义Cahn-Hilliard模型上
On a generalized Cahn-Hilliard model with p-Laplacian
论文作者
论文摘要
考虑了在无升边界条件的真实线的界间隔内的广义Cahn-Hilliard模型。标签“概括”是指我们考虑浓度依赖性移动性，$ p $ - laplace运算符，带有$ p> 1 $的运营商，以及$ f（u）= \ frac {1} {2θ} {2θ} | 1-u^2 |^θ$的双重井潜力，带有$θ> 1 $；这些术语分别替换为持续的移动性，线性拉普拉斯操作员和$ c^2 $潜在的$ f“（\ pm1）> 0 $，这是标准的cahn-hilliard模型的典型代表。在调查了相关的固定问题并突出了标准结果的差异之后，我们将注意力集中在$ queq $ ge时，我们将注意力集中在$ qe $ pe $ pe $ qe q $ qe时。 $θ= p> 1 $，我们证明$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ MOTION $具有过渡层结构，从而扩展了标准模型的良好知识结果，其中$θ= P = 2 $，在$ superecitial $ case $ ch $θ> p> p> p> p> 1 $中
A generalized Cahn-Hilliard model in a bounded interval of the real line with no-flux boundary conditions is considered. The label "generalized" refers to the fact that we consider a concentration dependent mobility, the $p$-Laplace operator with $p>1$ and a double well potential of the form $F(u)=\frac{1}{2θ}|1-u^2|^θ$, with $θ>1$; these terms replace, respectively, the constant mobility, the linear Laplace operator and the $C^2$ potential satisfying $F"(\pm1)>0$, which are typical of the standard Cahn-Hilliard model. After investigating the associated stationary problem and highlighting the differences with the standard results, we focus the attention on the long time dynamics of solutions when $θ\geq p>1$. In the $critical$ $θ=p>1$, we prove $exponentially$ $slow$ $motion$ of profiles with a transition layer structure, thus extending the well know results of the standard model, where $θ=p=2$; conversely, in the $supercritical$ case $θ>p>1$, we prove $algebraic$ $slow$ $motion$ of layered profiles.
