四阶强阻尼非线性波动方程的整体W^(k,p)解

Global W^(k,p) Solutions of Strong Damped Nonlinear Wave Equations of Four Order

证明四阶强阻尼非线性波动方程的初边值问题utt-Δu -αΔut-εΔutt+ f ( u) =0 (α≥ 0 ,ε>0 ) ,u( x,0 ) =u0 ( x) , ut( x,0 ) =u1( x) ,u| Ω =0的整体广义解的存在惟一性 .利用“逐次磨光法”证明其整体 W2 ,p与 Wk,p的存在性 ,并讨论其整体古典解的存在性 .

This paper proves the existence and uniqueness of the global generalized solutions of the initial boundary value problem of strong damped nonlinear wave equations of fourth orderu tt - Δ u-α Δ u t-ε Δ u tt +f(u)=0 (α≥0, ε>0), u(x,0)=u 0(x), u t(x,0)=u 1(x), u| Ω =0and the existence of global W 2,p solutions and W k,p solutions by using successive molification, finally the existence of global classical solutions is discussed.