反应-对流-扩散方程组的齐次Dirichlet外区域问题的Fujita型定理  

Fujita-Type Theorem for Homogeneous Dirichlet Problems in Exterior Domain of Reaction-Convection-Diffusion Systems

作　　者：郭微[1] 王立波[1] GUO Wei WANG Libo(School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2017年第2期251-256,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金数学天元基金(批准号:10926169);2017年吉林省教育厅"十三五"科学技术研究项目

摘　　要：利用能量比较方法和比较原理考虑含源和对流项的耦合非线性扩散方程组的齐次Dirichlet外区域问题解的整体存在和爆破性质,确定了临界Fujita曲线,并建立了Fujita型爆破定理.结果表明,该临界Fujita曲线依赖于方程组的空间维数、对流项和反应项.Using the energy comparison method and comparison principle,we considered the global existence and blow up properties of the homogeneous Dirichlet problems in exterior domain of coupled nonlinear diffusion systems with reactions and convections,determined the critical Fujita curve and established the Fujita-type blow up theorem.The results show that the critical Fujita curve depends on the spacial dimension,convection and reaction terms of the systems.

关 键 词：反应-对流-扩散方程组 渐近行为 临界Fujita曲线 

分 类 号：O175.23[理学—数学]