摘要
利用Duhamel原理和Fourier变换将求解方程中的Cauchy问题转化为等价的积分方程,应用L^2理论,引入加权空间,对具有弱阻尼项的半线性梁方程的线性Cauchy问题作出衰减估计,以便于研究在小初值情形下,得到非线性方程的Cauchy问题整体解的存在性及唯一性.
Firstly, we apply Duhamel principle and Fourier transform to itsequivalent integral equation, Secondly, in the L^2 - theory, we lead into weightedspace, making up the decay estimate of The linear Cauchy Problem for the semilinear Beam equa. tion with damped term,in order to study the existence and uniqueness of global solutions for Nonlinear Evolution Equations in the case of small initial values.
出处
《枣庄学院学报》
2017年第5期49-57,9,共10页
Journal of Zaozhuang University
关键词
L^2理论
加权空间
弱阻尼项
衰减估计
the L^2 - theory
weighted space
damped term
the decay estimate
