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| 摘要: |
| 本文研究一类带有记忆项的双阻尼σ-发展方程的柯西问题.借助方程线性问题的衰减估计,利用压缩映像原理证得小初值问题解的整体存在性.同时考虑初值积分为正的情形,利用检验函数方法得到解的爆破以及生命跨度上界的估计.推广了带有双阻尼项的σ-发展方程的有关结论. |
| 关键词: σ -发展方程 双阻尼 记忆项 整体存在性 爆破 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金资助(11701477,11971394). |
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| GLOBAL EXISTENCE AND BLOW UP OF SOLUTIONS FOR A CLASS OF DOUBLE DAMPED σ-EVOLUTION EQUATIONS WITH MEMORY TERM |
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LIU Mei,HE Xin-hai,YANG Han
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| Abstract: |
| The purpose of this paper is to study the Cauchy problem for a class of double damped σ-evolution equations with memory term.With the help of the decay estimates of the corresponding linear problem,the global existence of the solution of the small initial value problem is obtained by using the contraction mapping principle.Moreover,when the integral of initial value is positive,the blow up of the solution and the upper bound of the lifespan are obtained by using the test function method.The conclusion on the sigma-evolution equation with double damping term is generalized. |
| Key words: σ -evolution equation double damping memory term global existence blow-up |
