论文标题:一类退化抛物方程组正解的整体存在性和爆破
Blow-up and Global Existence for a Degenerate Parabolic System
论文作者
论文导师 穆春来,论文学位 硕士,论文专业 应用数学
论文单位 四川大学,点击次数 132,论文页数 22页File Size372K
2006-03-10论文网 http://www.lw23.com/lunwen_18076472/
Blow up; global existence; upper estimate; degenerate parabolic system
该论文研究一类具有齐次Dirichlet边界条件的退化抛物方程组正解的性质,证明了所有正解整体存在的充要条件是12≥abλ,其中λ1是具有齐次Dirichlet边界条件的? ?在?上的第一特征值。同时,给出了一个解在有限时间发生爆破的充分条件,以及爆破时间的上界估计。
In this thesis, we consider positive solutions of a degenerate parabolic system with homogeneous Dirichlet boundary condition. It is proved that all positive solutions exist globally iff 12≥abλ, whereλ1 is the first eigenvalue of ? ? on ? with homogeneous Dirichlet boundary condition. At the same time, we also give a sufficient condition that a solution blows up in finite time and an upper estimate of maximal existence time.
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