一类非线性双曲方程整体弱解的存在性与不存在性

Existence and Nonexistence of Solution for a Class Nonlinear Hyperbolic Equation

讨论了一类非线性双曲方程utt-a1△u-a2 ∑ni=1 xi(｜uxi｜m - 1uxi) -a3 △ut =0的初边值问题整体弱解的存在性与不存在性和指数衰减 .

We discuss the following nonlinear hyperbolic equationu tt -a 1△u-a 2∑ni=1x i(|u x i | m-1 u x i )-a 3△u t=0with the initial boundary value problem, we give the condition of existence and nonexistence for the global solution and the energy decay.