On the stability of the solutions of linear stochastic integro-differential equations encountered in elasticity and viscoelasticity problems |
| |
| Institution: | 1. Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 100084, China;2. Joint Center for Global Change Studies, Beijing 100875, China;3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (SAR), China;4. Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA 30303, United States;5. Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, United States;1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, PR China;2. School of Science, Lanzhou University of Technology, Lanzhou, PR China;1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710062, China;2. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China;1. School of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China;2. School of Computer and Control Engineering, Yantai University, Yantai, Shandong 264005, China;1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, PR China;2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, PR China |
| |
| Abstract: | The asymptotic stability, almost sure also in the mean square, of a viscoelastic system subjected to a load in the form of a random stationary broadband ergodic process is investigated. The behaviour of this system is described by integro-differential equations with stochastic parameters. The stability is considered with respect to the perturbation of the initial conditions. The governing relation is taken in an integral form with a creep (or relaxation) kernel of convolution type, which satisfies the condition of limited creep of the material. Using the fundamental solution of the corresponding deterministic integro-differential equation and its maximum Lyapunov exponent, the sufficient condition for stability of the zero solution of the initial equation or, which is the same thing, the equilibrium position of the viscoelastic system, is obtained. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
