摘要
讨论下列初边值问题utt+uxxxx-∫t0λ(t-τ)uxxxx(x,τ)dτ=g(u)+h(ut),0<x<L,t>0u|x=0=u|x=L=0,t≥0uxx|x=0=uxx|x=L=0,t≥0u|t=0=φ(x),ut|t=0=ψ(x),0≤x≤L在一定条件下,证明了这个问题整体经典解的存在性、唯一性和稳定性。
The global classical solutions of the following problem were studied u tt +u xxxx -∫ t 0λ(t-τ)u xxxx (x,τ) d τ=g(u)+h(u t),0<x<L,t>0 〖HJ*4]u| x=0 =u| x=L =0,t≥0 u xx | x=0 =u xx | x=L =0,t≥0 u| t=0 =φ(x),u t| t=0 =ψ(x),0≤x≤L under certain conditions on g,h and λ,the unique existence and stability of the global classical solution of this problem could be obtained.
出处
《甘肃科学学报》
1999年第1期26-30,共5页
Journal of Gansu Sciences
关键词
定解问题
经典解
存在性
积分项
粘弹性梁方程
beam equation,problem of determining solution,classical solution,existence