具有阻尼和非线性对数源项的波方程能量衰减  

Energy Decay of Wave Equation with Damping Terms and Nonlinear Logarithmic Source Term

作　　者：武福敏 郝江浩[1] WU Fumin;HAO Jianghao(School of Mathematical Science,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《河南科技大学学报（自然科学版）》2022年第4期92-97,M0008,共7页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11871315)。

摘　　要：研究具有线性强阻尼、非线性弱阻尼和非线性对数源项波方程解的存在性和能量衰减。在合适的假设条件下,通过势阱方法和Lyapunov泛函方法分别证明了在初始能量小于阱深、等于阱深两种情形下系统能量的指数衰减。The existence of the solution and energy decay for the wave equation with strong linear damping,weak nonlinear damping and nonlinear logarithmic source term were studied.Under appropriate assumptions,the exponential decay of the system energy is proved by the potential well method and Lyapunov functional method when the initial energy is less than the well depth and equal to the well depth,respectively.

关 键 词：波方程 强阻尼 弱阻尼 非线性源项 能量衰减 

分 类 号：O175.2[理学—数学]