无界区域中的非线性双曲型方程

On Nonlinear Hyperbolic Equation in Unbounded Domain

本文研究无界区域中的非线性双曲方程u_(tt)+A^2u+M(x,||A u||_2~2)Au=0这类问题的模型来自梁的横向挠曲方程.本文利用不动点方法结合能量估计证明了当M与x有关时,上述方程局部解的存在唯一性.

The following nonlinear hyperbolic equation is discussed in this paper. where,The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.