| 许勇强.带有非线性记忆的阻尼双曲方程组全局解的存在性与非存在性[J].数学年刊A辑,2012,33(5):557~578 |
| 带有非线性记忆的阻尼双曲方程组全局解的存在性与非存在性 |
| Existence and Nonexistence of Global Solutions to a Damped Hyperbolic System with Nonlinear Memory |
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| DOI： |
| 中文关键词: 双曲方程组 非线性 存在与非存在性 全局解 |
| 英文关键词:Hyperbolic system, Nonlinear, Existence and nonexistence, Global
solution |
| 基金项目:国家自然科学基金(No10976026)资助的项目 |
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| 中文摘要: |
| 首先研究了带有非线性记忆的双曲方程组解的局部存在性.然后,在N=1的情况下,证明了小初值解的全局存在性,并给出了当t→∞时的渐近性态.最后在N≥1且初值是正的情况下,导出了全局解的非存在性结果. |
| 英文摘要: |
| The author studies the local existence of the solutions to a damped hyperbolic
system with nonlinear memory. The global existence and the asymptotic behavior as t→∞
of solutions with small initial data are established in the case N = 1. Moreover, a nonexistence
result of global solutions with some positive initial data is obtained for N ≥ 1. |
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