摘要
运用PotentialWell方法研究了一类四阶非线性波动方程初边值问题整体解的不存在性 .首先定义了该问题的位势深度d ,然后运用索伯列夫空间中的嵌入定理结合Sobolev Hardy不等式证明位势深度d >0 ,再恰当地构造能量函数E(t) ,运用反证法证明了该问题整体解的不存在性 .当初值满足K(u0 ) <0 ,J(u0 ) <d ,E( 0 ) <d时 ,该问题没有整体解 .这里的K(·)和J(·)是2个泛函 .
The global nonexistence of a fourth order wave equation is studied using Potential Well method. Potential depth of this problem is defined first. By using Sobolev-Hardy inequality and the theory of embedding in Sobolev space, it is proved that the potential depth is a positive number. Finally, the energy function E(t) is appropriately constructed global nonexistence is verified by using reduction to absurdity. It is shown that the problem has no global solution when its initial value satisfy K(u 0)<0,J(u 0)<d,E(0)<d. Here K(·) and J(·) are two functions.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2004年第5期690-693,共4页
Journal of Southeast University：Natural Science Edition
