一类四阶非线性波动方程的初边值问题

On the Initial-Boundary Value Problems for a Class of Nonlinear Wave Equations of Fourth-Order

利用 Galerkin 方法证明一类四阶非线性波动方程W_(tt)-[a_0(t)+a_1(x,t)(W_x)^(a-1)]W_(xx)-a_2(t)W_(xx t)=f(x,t,W,W_x,W_t,W_(xt))的第一,第二和混合非齐次初边值问题解的存在性、唯一性和稳定性。

In this paper,the existence,uniqueness and stability of the solutions for the first,the second and the mixed non-homogenous initial-boundary value problems of the nonlinear wave e-quation of fourth-orderW_u-[a_0(t)+a_1(x,t)(W_x)^(n-1))W_(xx)-a_2(t)W_(xxtt)=f(x,t,w,w_x,w_t,w_(xt))are proved by Galerkin method.