| 关于一个反应扩散方程解的讨论 |
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| 引用本文： | 尚亚东.关于一个反应扩散方程解的讨论[J].西安石油大学学报(自然科学版),1990(4). |
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| 作者姓名： | 尚亚东 |
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| 作者单位： | 兰州大学数学系 研究生 |
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| 摘 要： | 本文讨论了燃烧理论中提出的问题U_1=U_(xx)+λe~u,U|=0及U|=φ(X)的定常解的存在性、唯一性及爆破解的存在性,用不同于他人的分析方法给出了这一方程组存在定常解时的λ范围及定常解存在时的解析表达式;给出了定常解唯一的一个充分条件,在更强的不等式代换下得到了它的解发生爆破现象的两个充分条件,本文部分结果对λ=λ(x)为函数时仍然成立,对此我们仅将结论附在λ为常数时相应结果后面。
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| 关 键 词： | 反应扩散方程解 定常解 唯一性 爆破解 |
Discussion on the Solutions of a Reacting and Diffusing Equation |
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| Shang Yadong.Discussion on the Solutions of a Reacting and Diffusing Equation[J].Journal of Xian Shiyou University,1990(4). |
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| Authors: | Shang Yadong |
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| Institution: | Lanzhou University |
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| Abstract: | This paper discusses the existance and uniqueness of the stationary solutions and the existance of blowing up solutions of the problem:The range of λ and the analytic expressions are given while the stationary solutions exist in the above problem by using a analytical method. The paper gives the unique sufficient conditions for the stationary solution. Two sufficient conditions for the blowing up solutions under stronger inequality replacement are obtained. Some results of this paper still hold true when λ=λ(x)is a function. Thus the conclusions will follow the corresponding results when λ is a constant. |
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| Keywords: | reacting and diffusing equation solution stationary solution uniqueness blow-up solution |
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