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| 摘要: |
| 本文研究了一类竞争型反应扩散方程的时间最优控制问题的存在性问题.利用上下解的方法，得到了反应扩散方程正解的存在性.利用Kakutani不动点定理，证明了反应扩散方程关于正轨迹的局部精确能控性，并据此证明了时间最优控制的存在性. |
| 关键词: 正解 能控性 时间最优控制 反应扩散方程 |
| DOI： |
| 分类号:O211.4 |
| 基金项目:国家自然科学基金资助（61573012）. |
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| POSITIVE SOLUTIONS AND TIME OPTIMAL CONTROL PROBLEMS FOR A COMPETITIVE REACTION-DIFFUSION EQUATION |
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LIU Yuan-kai,ZHANG Liang
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| Abstract: |
| This work is concerned with the time optimal control problem of a competitive reaction-diffusion. By the method of upper and lower solutions, we get the existence of positive solutions, which is set as the positive trajectory in establishing the local exact controllability by Kakutani’s fixed point theorem. Upon this result, the existence of time optimal control for the reaction-diffusion is proved. |
| Key words: positive solution controllability time optimal control reaction-diffusion equation |
