On a viscous fourth-order parabolic equation with boundary degeneracy

被引：0
|
作者：
Liang, Bo [1 ]
Su, Caiyue [1 ]
Wang, Ying [1 ]
Li, Xiumei [1 ]
Zhang, Zhenyu [2 ]
机构：
[1] Dalian Jiaotong Univ, Sch Sci, Dalian 116028, Peoples R China
[2] Dalian Jiaotong Univ, Sch Automat & Elect Engn, Dalian 116028, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2022年 / 2022卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fourth-order degenerate; Boundary degeneracy; Double degeneracy; GLOBAL EXISTENCE; BLOW-UP;
D O I：
10.1186/s13661-022-01609-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A viscous fourth-order parabolic equation with boundary degeneracy is studied. By using the variational method, the existence of a time-discrete fourth-order elliptic equation with homogeneous boundary conditions is solved. Moreover, the existence and uniqueness for the corresponding parabolic problem with nondegenerate coefficient is shown by several asymptotic limit processes. Finally, by applying the regularization method, the existence and uniqueness for the problem with degenerate boundary coefficient is obtained by applying the energy method and a small parameter limit process.
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页数：16
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