Global existence of weak solutions to a class of higher-order nonlinear evolution equations
This paper deals with the initial boundary value problem for a class of n-dimensional higher-order nonlinear evolution equations that come from the viscoelastic mechanics and have no positive definite energy. Through the analysis of functionals containing higher-order energy of motion, a modified po...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024248 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This paper deals with the initial boundary value problem for a class of n-dimensional higher-order nonlinear evolution equations that come from the viscoelastic mechanics and have no positive definite energy. Through the analysis of functionals containing higher-order energy of motion, a modified potential well with positive depth is constructed. Then, using the potential well method, and Galerkin method, it has been shown that when the initial data starts from the stable set, there exists a global weak solution to such an evolution problem. |
|---|---|
| ISSN: | 2688-1594 |