燃烧理论中一个反应扩散方程组的初值问题解的存在性唯一性及其渐近性质

燃烧理论中一个反应扩散方程组的初值问题解的存在性唯一性及其渐近性质 ON THE EXISTENCE UNIQUENESS AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A REACTION DIFFUSION SYSTEM IN COMBUSTION THEORY 宋开泰 Song kaitai first-author 本文讨论了由燃烧理论中的一个反应网络所得到的反应扩散方程组的初值问题。我们得到了解的存在性与唯一性,并讨论了当t→∞时,解的渐近性质。 In this paper we discuss the following initial-value preblem It Comes from a reaction network in Combustion theory, we assume that T 0 （x）≥0, Y j,o （x）≥0 are Piecewise continuous and bounded in x∈R; h i （T） （i=1, 2）and its derivaives are continuous and satisfy Our main results are the following theorems Theorem 2.4. Under foregoing hypothesis, the initial—value problem （2.1）、（2.2） has a unique and bounded solution in an arbitrary strip domain Q T - = {（x,t）|x∈R,0 < t < T < ∞}. Moreover we consider also the asymptotic behavior of the solution as t→∞. we have Theorem 3.1. Assume U=（T, Y 1 , Y 2 , Y 3 ） is a solution o the Cauehy Problem （2.1）、（2.2）, and let and 0≤Y j,o （x）≤1 if |x|≤L j , Y j （x）=1 if |x| > L j ,j=1,2,3. thea we have lim T（x,t）=0, lim Y j,o （x,t）=1,j=1,293, and the convergence is uniform in x∈R. 中国科学院科学基金 1985-02-01 2021-04-01 2