带变指标反应项的非线性抛物方程正解的爆破

Blow-up of Solutions to Nonlinear Parabolic Equations with Variable Exponents in Reaction Term

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.

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.