一类具有非线性异号源项波动方程的初边值问题

Initial Boundary Value Problem for Wave Equations with Nonlinear Source Terms of Different Signs

研究具有两个异号非线性源项波动方程的初边值问题utt+Δ2u+αut+a|u|p-1u-b|u|q-1u=0(α>0,a>0,b>0).该方程用以描述具有两个性质相异的源作用下的物理系统.利用Galerkin方法证明了若1≤n≤4时,1<q<p<∞;n≥5时,1<q<p<nn-+44,u0(x)∈H02(Ω),u1(x)∈L2(Ω),则问题存在一个整体弱解u(x,t)∈L∞(0,T;H20(Ω)).

The initial boundary value problem for wave equations with two nonlinear source terms of different signs utt＋Δ2u＋αut＋a｜u｜p-1u-b｜u｜q-1u=0（α0,a0,b0） is studied in this paper.This equation describes physical systems are affected by two sources with different properties.It is proved that if 1≤n≤4,1qp∞;n≥5,qqpn＋4n-4,u0（x）∈H20（Ω）,u1（x）∈L2（Ω）,then the problem admits exist the global weak solution u（x,t）∈L∞（0,T;H20（Ω）） by using Galerkin method.