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| 摘要: |
| 该文研究具有多项式非线性项和粘性项的非线性抛物方程的初边值问题.在一定条件下, 我们得到方程的弱解全局存在. 在另一些条件下, 我们得到该方程的解将在有限时刻爆破, 并给出了爆破时间的上界, 该上界受初始函数及其支集控制. 该结论推广了Messaoudi在文献[15, 16]中的工作. |
| 关键词: 多项式非线性 粘弹性项 存在性 爆破性 |
| DOI： |
| 分类号:O175.26 |
| 基金项目:国家自然科学基金(11601402)和中央高校基本科研业务费专项资金基金资助(2020IA003) |
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| EXISTENCE AND BLOW-UP OF SOLUTIONS OF A PARABOLIC EQUATION WITH VISCOELASTIC TERM |
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DU Yu-ge,TIAN Shu-ying
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| Abstract: |
| This paper studies the initial boundary value problem of a viscoelastic equation with polynomial nonlinearity. Under certain conditions, the existence of global weak solution is given. Under other conditions, the solution of the equation will blow up at a finite time and the upper bound for blow-up time is obtained. The upper bound is controlled by the initial data and its support. This result extends the work of Messaoudi in [15, 16]. |
| Key words: polynomial nonlinearity viscoelastic term global existence blow-up |
