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| Gray-Scott模型非常值正稳态解的不存在性 | |
| 引用本文： | 李莹,周文书.Gray-Scott模型非常值正稳态解的不存在性[J].大连民族学院学报,2016,18(3):233-236. |
| 作者姓名： | 李莹 周文书 |
| 作者单位： | 1.北方民族大学 数学与信息科学学院,宁夏 银川750021; 2.大连民族大学 理学院,辽宁 大连116605 |
| 基金项目： | 国家自然科学基金项目(11571062); 辽宁省优秀人才支持计划(LJQ2013124); 中央高校基本科研业务费专项资金资助项目(DC201502050202)。 |
| 摘 要： | 研究了具Neumann边界条件的Gray-Scott模型非常值正稳态解的不存在性。首先,借助于极值原理、Harnack不等式和先验估计技巧,得到了正解的上、下界;其次,利用积分平均方法,推导出了一个新的积分恒等式;最后,利用上述结果并结合Poincaré不等式,给出了不存在非常值正解的若干充分条件。 |
| 关 键 词： | Gray-Scott模型 稳态解 不存在性 |
Nonexistence of Positive Nonconstant Stationary Solutions for the Gray-Scott Model |
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| LI Ying,ZHOU Wen-shu.Nonexistence of Positive Nonconstant Stationary Solutions for the Gray-Scott Model[J].Journal of Dalian Nationalities University,2016,18(3):233-236. | |
| Authors: | LI Ying ZHOU Wen-shu |
| Institution: | 1.School of Mathematics and Information Sciences, Beifang University of Nationalities, Yinchuan Ningxia 750021, China; 2.School of Science, Dalian Minzu University, Dalian Liaoning 116605, China |
| Abstract: | This paper is devoted to the nonexistence of positive nonconstant stationary solutions for the Gray-Scott model with Neumann boundary conditions. Firstly, the upper and lower bounds of positive solutions for the problem are obtained by means of Maximal principle, Harnack inequality and a prior estimating techniques. Secondly, a new integral identity of positive solutions is established by integral mean method. Finally, through Poincaré inequality and the results above, some sufficient conditions of nonexistence of positive solutions are given. |
| Keywords: | Gray-Scott model stationary solution nonexistence |
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