| 摘要: |
| 本文研究了一类带有非线性范数型源的反应扩散方程组ut=△um+a||up1vq1||αr1，vt=△vn+b||vp2wq2||βr2，wt=△wh+c||wp3uq3||γr3在齐次Dirichlet边界条件下解的爆破问题.利用上下解方法和构造辅助函数的技巧，得到了方程组解的整体存在与爆破的准则，将当前的一些研究结果推广到更复杂的情形. |
| 关键词: 反应扩散方程组 范数型源 整体存在 爆破 |
| DOI： |
| 分类号:O175.2 |
| 基金项目:国家自然科学基金资助（11171135；51276081）；江苏省自然科学基金资助（14KJA110001）. |
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| BLOW-UP PROPERTIES FOR A REACTION-DIFIUSION SYSTEM WITH NONLINEAR NORM-TYPE SOURCES |
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ZHONG Guang-sheng1,2, TIAN Li-xin2
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1.School of Science, Nantong University, Nantong 226007, China;2.Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
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| Abstract: |
| In this paper, we study the blow-up problems for a class of reaction-difiusion system with nonlinear norm-type sources:ut=△um+a||up1vq1||αr1,vt=△vn+b||vp2wq2||βr2,wt=△wh+c||wp3uq3||γr3 subject to homogeneous Dirichlet conditions. By using upper-lower solution method and constructing auxiliary functions' techniques, we obtain the criteria for global existence or finite time blow-up, which extend some results of the current research to more complex situations. |
| Key words: reaction-difiusion system norm-type sources global existence blow up |
