论文标题
在较小的沉积速率的情况下
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
论文作者
论文摘要
我们显示了解决六阶对流Cahn-Hilliard方程的解决方案的稳定。 {问题}具有梯度流的结构，该梯度流以系数$δ> 0 $的二次不稳定项扰动。通过Carvalho-Langa-Robinson应用抽象结果，我们表明，对于小$δ$，方程在弱的意义上具有梯度流的结构。在途中，我们证明了一种用于抛物线问题的永恒解决方案的Liouville定理。最后，由于Hale-Raigel，所需的稳定是从强大的定理开始的。
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising term with coefficient $δ>0$. Through application of an abstract result by Carvalho-Langa-Robinson we show that for small $δ$ the equation has the structure of gradient flow in a weak sense. On the way we prove a kind of Liouville theorem for eternal solutions to parabolic problems. Finally, the desired stabilisation follows from a powerful theorem due to Hale-Raugel.
