一类非线性双曲方程的局部解

The Local Solution for a Class of Nonlinear Hyperbolic Equation

研究如下非线性双曲方程的初边值问题utt-m(‖ u‖22)Δu-γΔut=β｜u｜αu,其中α>0,γ 0,β>0,α,β,γ均为常数.利用Galerkin方法和改进的势井理论:当m(s)和α满足一定的条件,且初值充分小时,证明了该方程局部解的存在性和唯一性.

In this paper, we consider an initial-boundary value problem of the following nonlinear hyperbolic equationu_tt-m(‖u‖~2_2)Δu-γΔu_t=β|u|_αu.By using of Galerkin method and modified potential well theory, the well-posedness theory is established under some assumptions of m(s), and initial data.