分布阻尼下非线性梁光滑解的存在性

摘要

该文研究一个描述梁振动的非线性模型,主要研究该模型在分布阻尼下局部光滑解的存在性.首先应用发展方程理论证明相关线性系统存在光滑解,然后由一系列能量估计结合不动点定理证明所考察的非线性系统局部光滑解的存在性.%This article is devoted to the study of the existence of local smooth solutions to a nonlinear beam with distributed damping. Applying the theory of evolution equations, we first show that related linear systems admit unique smooth solutions. Then some energy estimates for the linear systems are established. Finally we prove the existence of local smooth solutions to the nonlinear system by the fixed point argument.