一类多重耦合变指数抛物方程组的爆破解研究（英文）  

Blow-Up Solutions of Heat Equations with Multi-Coupled Nonstandard Growth Sources

作　　者：李锋杰 孙玺政 杜旖旎 LI Fengjie;SUN Xizhengl;DU Yini(College of Science,China University of Petroleum,Qingdao 266580,China;High-Tech Material of Aluminium and Application Technology,Binzhou 256200,China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580 [2]苏州大学与魏桥铝业高端铝材应用科技研究所,山东滨州256200

出　　处：《应用数学》2018年第4期803-819,共17页Mathematica Applicata

基　　金：Supported by Shandong Provincial Natural Science Foundation,China(ZR2016AM12,ZR2017LA003)

摘　　要：在本文中,我们考虑一类具有非标准增长条件的多重耦合热传导方程组的齐次第一初边值问题.首先,我们研究古典解的存在唯一性,其次,我们讨论了解的爆破指标和解的整体存在性质,进一步,我们区分解的同时与不同时爆破现象,有趣的是变指数不仅仅可以区分解的爆破和整体存在而且可以区分解的同时与不同时爆破,最后,对于同时爆破的情形,在对系数和指数做一些合理假设下,我们得到解在区域上每个点都发生爆破的现象.In this paper, we consider the homogeneous Dirichlet problem of heat equations involving multi-coupled nonstandard growth sources. Firstly, we study the existence of classical solutions. Secondly, we prove the criteria on the blow-up and global existence of solutions, respectively. Furthermore, we classify simultaneous and non-simultaneous blow-up phenomena for the components of solutions. It is interesting that the variable exponents play an important role not only in distinguishing global and blow-up solutions,but also in classifying the non-simultaneous blow-up phenomena of components. Moreover,for the simultaneous blow-up solutions, we prove that blow-up occurs everywhere in the space domain under some conditions on the variable exponents and coefficients.

关 键 词：非标准增长条件 变指数 不同时爆破 整体存在 爆破集 

分 类 号：O175.2[理学—数学]