关于双曲型方程解的爆破

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.