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。
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.
出处
《西安石油学院学报》
1990年第4期77-85,共9页
Journal of Xi'an Petroleum Institute
关键词
反应扩散方程
定常解
唯一性
燃烧
reacting and diffusing equation solution
stationary solution
uniqueness
blow-up solution
