In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitabl...In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.展开更多
We consider a von Karman equation of memory type with a delay term . By introducing suitable energy and Lyapunov functional, we establish a general decay estimate for the energy, which depends on the behavior of g.
In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and exist...In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for yon Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.展开更多
In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainl...In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finitedimensional global attractor.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(20110007870)
文摘In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.
文摘We consider a von Karman equation of memory type with a delay term . By introducing suitable energy and Lyapunov functional, we establish a general decay estimate for the energy, which depends on the behavior of g.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(2014R1A1A3A04049561)
文摘In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for yon Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of ScienceICT and Future Planning(Grant No.2014R1A1A3A04049561)
文摘In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finitedimensional global attractor.
