一类非线性波动方程混合问题解的爆破

Blow-up of the Solution to the Mixed Problem of Some Nonlinear Wave Equations

依据势井理论,通过构造不稳定集,应用经过改进的凸性分析方法,简明地证明了一类非线性波动方程uu-△u=|u|γ-1u的混合问题解的爆破性质,即当初值属于不稳定集,初始能量为正但有适当上界时,解在L2范数意义下在有限时刻发生爆破.

According to the potential well theory,the blowup property of the solution for the mixed problem of some nonlinear wave equations utt-Δu = |u|γ-1u is proved in a simple way by constructing unstable set and using the revised convexity method. Roughly speaking, when the initial data stay in the unstable set and the initial energy has properly positive upper bound, the solution will blow up in finite time under the L2 norm.