具有对数源项和时滞的波方程解的稳定性  

Stability of Wave Equation with Logarithmic Source Term and Delay

作　　者：郝江浩[1] 赵力菲 HAO Jianghao;ZHAO Lifei(School of Mathematical Sciences,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：《山西大学学报（自然科学版）》2022年第3期532-542,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11871315)。

摘　　要：在偏微分方程建模问题中,对数源项问题广泛存在于膨胀宇宙学、超对称场论和量子力学中。文章研究具有对数源项、动力学边界条件和时滞的波方程初边值问题解的稳定性。在合适的假设条件下,通过构造稳定集和Lyapunov泛函,利用乘子法和能量扰动法给出了具对数源项和时滞的波方程解的稳定性。In the modeling of partial differential equations,logarithmic source term problems widely exist in inflation cosmology,super-symmetric field theory and quantum mechanics.In this paper,we consider a wave equation with logarithmic source term,dynamic boundary conditions and delay.We give the existence and stability of solution.Under appropriate assumptions,the stability of system with logarithmic source term and delay is obtained by constructing stable set and Lyapunov functional,using multiplier method and energy perturbation method.

关 键 词：波方程 对数源项 动力学边界条件 时滞 稳定性 

分 类 号：O175.2[理学—数学]