The authors show the existence and uniqueness of solution for a class of stochastic wave equations with memory. The decay estimate of the energy function of the solution is obtained as well.
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
We study the large time behavior of a 3-D MHD(magneto-hydrodynamical)-type system without magnetic diffusion introduced by Lin and Zhang(2014). By using the elementary energy method and interpolation technique, we pro...We study the large time behavior of a 3-D MHD(magneto-hydrodynamical)-type system without magnetic diffusion introduced by Lin and Zhang(2014). By using the elementary energy method and interpolation technique, we prove the global existence and decay estimate of smooth solution near the equilibrium state(x3, 0).展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10871103)
文摘The authors show the existence and uniqueness of solution for a class of stochastic wave equations with memory. The decay estimate of the energy function of the solution is obtained as well.
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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371039 and 11425103)
文摘We study the large time behavior of a 3-D MHD(magneto-hydrodynamical)-type system without magnetic diffusion introduced by Lin and Zhang(2014). By using the elementary energy method and interpolation technique, we prove the global existence and decay estimate of smooth solution near the equilibrium state(x3, 0).
