CAJ | 학술논문

讨论了一类具有内层和初始层激波解的反应扩散方程初始边值问题.反应扩散方程的激波解,在核物理学、热力学,大气物理学,环境科学中有广泛的应用.本文首先引入伸长变量构造了问题解的内层和初始层.然后利用合成方法得到得到了解的形式渐近展开式.然后构造上、下解.最后利用微分不等式理论,证明了解的存在性和解的渐近展开式的一致有效性.
토론료일류구유내층화초시층격파해적반응확산방정초시변치문제.반응확산방정적격파해,재핵물이학、열역학,대기물이학,배경과학중유엄범적응용.본문수선인입신장변량구조료문제해적내층화초시층.연후이용합성방법득도득도료해적형식점근전개식.연후구조상、하해.최후이용미분불등식이론,증명료해적존재성화해적점근전개식적일치유효성.
@@@@In this paper, we consider a class of initial boundary value problem for the re-action diffusion equation, whose shock solution has the interior and initial layers. The shock solution of the reaction diffusion has wide applications in the nuclear physics, heat dynamics, atmospheric physics and environmental science. At first, we construct the interior and initial layers of solution. Then, we obtain the formal asymptotic expression of solution via the composed method. Next, we construct the super and lower solutions. Finally, by using the theory of differential inequalities, we prove the existence and uniform validity for the asymptotic expression of the solution.