|
|
- 2018
无界域上非自治Reaction-Diffusion方程的后向紧动力学
|
Abstract:
在非自治外力项是后向λ-缓增有限的和后向尾部渐近趋于零的假设条件下，运用cut-off函数、后向Granwall不等式、后向Granwall-type不等式获得了无界域上非自治Reaction-Diffusion方程拉回吸引子的后向紧性.
The backward compactness of attractors for non-autonomous reaction-diffusion equations on unbounded domains is obtained under the conditions of both backward λ-tempered finiteness and backward tail-smallness for the non-autonomous force by using a cut-off function, a backward Granwall inequality and a backward Granwall-type inequality
| [1] | YIN J Y, GU A H, LI Y R. Bankwards Compact Attrators for Non-Autonomous damped 3D Navier-Stoks Equations[J]. Dynamics of PDE, 2017, 14(2): 201-218. |
| [2] | WANG B X. Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-Compact Random Dynamical Systems[J]. J Differ Equ, 2012, 253(5): 1544-1583. DOI:10.1016/j.jde.2012.05.015 |
| [3] | CARVALHO A N, LANGA J A, ROBINSON J C. Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems[M]. New York: Springer, 2013. |
| [4] | SONG H T. Pullback Attractors of Non-Autonomous Reaction-Diffusion Equations in[J]. J Differ Equ, 2010, 249(10): 2357-2376. DOI:10.1016/j.jde.2010.07.034 |
| [5] | 佘连兵, 王仁海. 非自治Reaction-Diffusion方程后向紧的拉回吸引子的存在性[J]. 四川师范大学学报(自然科学版), 2017, 40(6): 1-5. |
| [6] | YIN J Y, LI Y R, GU A H. Backwards Compact Attractors and Periodic Attractors for Non-Autonomous Damped Wave Equations on an Unbounded Domain[J]. Comput Math Appl, 2017, 74(4): 744-758. DOI:10.1016/j.camwa.2017.05.015 |
| [7] | LI Y R, GU A H, LI J. Existence and Continuity of Bi-Spatial Random Attractors and Application to Stochastic Semi-Linear Laplacian Eequations[J]. J Differ Equ, 2015, 258(2): 504-534. DOI:10.1016/j.jde.2014.09.021 |
| [8] | LI Y R, YIN J Y. A Modified Proof of Pullback Attractors in a Sobolev Space for Stochastic Fitz Hugh-Nagumo Equations[J]. Disrete Contin Dyn Syst, 2016, 21(4): 1203-1223. DOI:10.3934/dcdsb |
| [9] | TEMAM R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]//Applied Mathematical Science Series. Berlin: Springer-Verlag, 1988. |
| [10] | LUKASZEWICZ G. On Pullback Attractors in for Non-Autonomous Reaction-Diffusion Equations[J]. Nonlinear Anal, 2010, 73(10): 350-357. |
| [11] | CUI H Y, LANGA J A, LI Y R. Regularity and Structure of Pullback Attractors for Reaction-Diffusion Type Systems Without Uniqueness[J]. Nonlinear Anal, 2016, 140: 208-235. DOI:10.1016/j.na.2016.03.012 |
| [12] | LI Y R, WANG R H, YIN J Y. Bankward Compact Attrators for Non-Autonomous Benjsmin-Bona-Mahony Equations on Unbounded Channels[J]. Discrete Contin Dyn Syst B, 2017, 22(7): 2569-2586. DOI:10.3934/dcdsb |
