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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。
In this paper, we discuss the existence and uniqueness of the solution to the problem of the combustion theory U_1 = U_ (xx) + λe ~ u, U | = 0 and U | = φ (X) For others, the analytic expression of the λ range and the existence of stationary solutions for this system of equations is given. The sufficient condition for the existence of stationary solutions is given. Two sufficient conditions for its solution to blowup are obtained. Some of the results in this paper are still valid for λ = λ (x), for which we only attach the conclusion to the corresponding result after λ is constant.