Asymptotic behavior of solutions to a fourth-order degenerate parabolic equation

被引：0

作者：

Kong, Linghua ^{[1
]}

Zhu, Yongbo ^{[2
]}

Liang, Bo ^{[3
]}

Wang, Ying ^{[2
]}

机构：

[1] Dalian Ocean Univ, Sch Informat Engn, Dalian, Liaoning, Peoples R China

[2] Dalian Jiaotong Univ, Sch Sci, Dalian, Liaoning, Peoples R China

[3] Chuzhou Univ, Sch Math & Finance, Chuzhou, Anhui, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING | 2024年 / 24卷 / 4-5期

关键词：

Fourth-order; large-time behavior; exponential decay; dissipative entropy; THIN-FILM EQUATIONS; LUBRICATION APPROXIMATION; VISCOUS FILMS; CONTACT-LINE; BLOW-UP; EXISTENCE; REGULARITY;

D O I：

10.3233/JCM-247227

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The decay behavior of a class of equation w(t) = -del center dot (w(n)del Delta w + alpha w(n-1) Delta w del w + beta w(n-2 vertical bar)del w(vertical bar 2)del w) is considered under the Neumann boundary condition. The equation can be viewed as a generalization of the thin film equation w(t) + (w(n) w(xxx))(x) = 0, which can be used to describe the movement of the skinny viscous layer of compressible fluid along the slope. We obtain that the solution decays exponentially in L-1-norm in the multi-dimensional case, and decays algebraically in L-infinity-norm in the one-dimensional case. The critical step solving the problem is to construct appropriate dissipative entropies.

引用

页码：2085 / 2094

页数：10