关于双曲型方程解的爆破
ABOUT BLOW UP OF THE SOLUTIONS OF THE HYPERBOLIC EQUATION
Abstract
在RN×R+(N≥2)中考虑非线性双曲型方程:utt-Di(aij(x)Dju)=|u|p-1u。Kato1980年证明了当1<P≤时,Cauchy问题的解可能在有限时刻爆破.本文使用不同的方法估计,把Kato的结果改进为1<P< The nonIinear hyperbolic equation in RN × R+ (N ≥ 2): utt-Di(aij(x)Dju)=|u|p-1u(x,t) is considered. In 1980, Kato proved that the solutions of Cauchy problemmay blow up in finite time if 1 < p ≤ . In the present work we win improve his resultallowing 1 < p < by using a dtherellt method.