一类具有变指数时滞项和源项的粘弹性方程解的爆破

Blow-Up of Solutions for an Extensible Viscoelastic Plate Equation with Time Delay and Variable Exponents

研究含变指数时滞项和源项的粘弹性方程:utt+△^(2)u-M(||▽u||^(2))△u+∫^(t)_(0)g(t-s)△u(s)ds+μ_(1)|ut(x,t)|^(r)(x)-2ut(x,t)+μ2|ut(x,t-τ)|^(r)(x)-2ut(x,t-τ)=|u|^(p)(x)-2u.利用凸性方法,证明了当该方程的初边值问题的初始能量为负值时,其能量解存在有限时间爆破.

In this paper,we study the extensible viscoelastic plate equation with time delay and variable exponents:utt+△^(2)u-M(||▽u||^(2))△u+∫^(t)_(0)g(t-s)△u(s)ds+μ_(1)|ut(x,t)|^(r)(x)-2ut(x,t)+μ2|ut(x,t-τ)|^(r)(x)-2ut(x,t-τ)=|u|^(p)(x)-2u.By the convexity method,we prove the energy solution of the equation blows up at finite time when the initial energy function is negative.