|
| 摘要: |
| 本文主要研究了一类双重退化的四阶抛物方程弱解的存在性问题.首先,利用Galerkin理论与能量估计方法可以得到该问题在非退化边界情形下弱解的存在性.在此基础上,通过对正则化问题的解进行一致估计以及渐近极限的过程，获得边界退化情形下弱解的存在性. |
| 关键词: 双重退化 非线性抛物型方程 边界退化 存在性 |
| DOI： |
| 分类号:O175.2 |
| 基金项目:国家自然科学基金(11201045),辽宁省教育厅高校科研项目资助(LJKMZ20220832). |
|
| EXISTENCE OF WEAK SOLUTIONS FOR A DOUBLY DEGENERATE FOURTH-ORDER PARABOLIC EQUATION |
|
LIANG Bo,LI Bin,MA Yong-feng
|
| Abstract: |
| In this paper, the existence of weak solutions for a doubly degenerate fourth-order parabolic equation is studied. By Galerkin process and energy method, the existence of the weak solutions in the non-degenerate case is proved firstly. On this basis, the existence of weak solutions in the degenerate case is obtained by uniform estimates asymptotic limits for the regularization problem. |
| Key words: doubly degeneracy Non-linear parabolic equation boundary degeneracy existence |
