一类非线性色散耗散波动方程的整体解

研究一类具有色散项与耗散项的四阶非线性波动方程在 n 维空间中有界域上的Dirichlet初边值问题.其中,半线性项 f(u)与u的符号相同.并满足一定的增长条件.定义了位势井W及一族位势井,证明了若满足一定的条件,则此问题存在一个整体弱解.且此解在这族位势井中.最后证明了整体强解的存在唯一性.

Global solutions for a class of nonlinear wave equations with dispersive-dissipative terms

The Dirichlet initial boundary value problem is studied for a class of nonlinear wave equations of fourth order with dispersive and dissipative terms on a bounded domain in n-dimensional space,where the sign of semi-linear term f(u) is the same as u and satisfies certain growth conditions.First,the potential well W and a family of potential wells are defined.Then it is proven that if certain conditions are satisfied,the problem has a global weak solution which belongs to the family of potential wells.Finally,the existence and uniqueness of global strong solution to this problem were proven.