Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems und...Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.展开更多
In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existenc...In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.展开更多
The present paper is devoted to the existence of the random attractor for partly dissipative stochastic lattice dynamical systems with multiplicative white noises.
文摘Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.
基金supported by Hunan Provincial Natural Science Foundation of China(No.2015JJ2144)National Natural Science Foundation of China(No.11671343 and No.11171280)+1 种基金the General Project of The Education Department of Hunan Province(No.12C0408)Zhejiang Natural Science Foundation(No.LY14A010012)
文摘In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.
基金supported by the National Natural Science Foundations of China(No.11071165,No.11071199)Natural Science Foundation of Guangxi(No.2013GXNSFBA019008)Department of Research Project of Guangxi Provincial(No.2013YB102)
文摘The present paper is devoted to the existence of the random attractor for partly dissipative stochastic lattice dynamical systems with multiplicative white noises.
