CAJ | 학술논문

研究了有界区域上的带变指标反应项的非线性抛物方程正解的爆破性质和整体存在性.通过构造适当的辅助函数,结合对空间区域的细致分析,利用特征函数法和不等式技巧,给出了其Dirichlet边值问题的正解产生爆破的充分条件.并利用上下解方法,证明了其整体解的存在性.
연구료유계구역상적대변지표반응항적비선성포물방정정해적폭파성질화정체존재성.통과구조괄당적보조함수,결합대공간구역적세치분석,이용특정함수법화불등식기교,급출료기Dirichlet변치문제적정해산생폭파적충분조건.병이용상하해방법,증명료기정체해적존재성.
In this paper,it was investigated that for Nonlinear parabolic equations with variable the blow-up and global existence of positive solutions exponentsin reaction term in bounded domain inRN . By constructing an appropriate auxiliary function, combining with a detailed analysis of the spatial re- gion and using the eigenfunction method and inequality technic on it, the sufficient conditions for blow-up positive solutions of the equations with Dirichlet boundary conditions were obtained. By using the method of upper and lower solutions, the existence of the global solutions was proved.