| 耦合抛物方程组正解的整体存在性与爆破 |
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| 引用本文： | 崔世泽,刘玉荣. 耦合抛物方程组正解的整体存在性与爆破[J]. 扬州大学学报(自然科学版), 2003, 6(3): 14-17,26 |
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| 作者姓名： | 崔世泽 刘玉荣 |
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| 作者单位： | 1. 常州工程职业技术学院,江苏,常州,213000
2. 扬州大学数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 国家自然科学基金(10171088) |
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| 摘 要： | 考虑带非线性边界条件αu/αn=u~α,αu/αn=v~β,(x,t)∈αΩ×(0,T)的耦合抛物方程组u_t=v~p△u,v_t=u~q△v,(x,t)∈Ω×(0,T),其中ΩR~N为一具有光滑边界的有界区域,p,q>0和α,β≥0为常数.研究了上述问题正解的整体存在性与不存在性,并建立了一条新的准则,证明了当且仅当α<1,β<1,且pq≤(1—α)(1-β)正解整体存在.
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| 关 键 词： | 耦合抛物方程组 整体存在性 有限时刻爆破 上解 下解 |
| 文章编号： | 1007-824(2003)03-0014-04 |
GLOBAL EXISTENCE AND BLOW UP OF SOLUTION TO A COUPLED PARABOLIC SYSTEM |
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| GUI Shi-ze LIU Yu-rong. GLOBAL EXISTENCE AND BLOW UP OF SOLUTION TO A COUPLED PARABOLIC SYSTEM[J]. Journal of Yangzhou University(Natural Science Edition), 2003, 6(3): 14-17,26 |
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| Authors: | GUI Shi-ze LIU Yu-rong |
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| Abstract: | This paper deals with coupled parabolic system ui=vp u,v,in (0,T) with nonlinear boundary conditions , where is a bounded domain with smooth boundary, p,q>0 and a,B>0 are constants. The criterion of global existence and nonexistence of positive solution is given. It is proved that the positive solution is global if and only if a<1, B<1 and pq<1<(1-a)(1-B). |
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| Keywords: | coupled parabolic system global existence blow up in finite time upper solution lower solution |
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