The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System
First, for a process U(t,τ)∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t)∣t≤T, for any T∈R, satisfying the following: (i) M(t) is compact, (ii) M(t) is positively invariant, that is, U(t,τ)M(τ)⊂M(t), and (iii) there exist k,l>0 s...
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Wiley
2016-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2016/1871602 |
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| author | Yongjun Li Xiaona Wei Yanhong Zhang |
| author_facet | Yongjun Li Xiaona Wei Yanhong Zhang |
| author_sort | Yongjun Li |
| collection | DOAJ |
| description | First, for a process U(t,τ)∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t)∣t≤T, for any T∈R, satisfying the following: (i) M(t) is compact, (ii) M(t) is positively invariant, that is, U(t,τ)M(τ)⊂M(t), and (iii) there exist k,l>0 such that dist(U(t,τ)B(τ),M(t))≤ke-(t-τ); that is, M(t) pullback exponential attracts B(τ). Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force. |
| format | Article |
| id | doaj-art-0434270feb1446a288009689e887c8d2 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-0434270feb1446a288009689e887c8d22025-02-03T06:00:21ZengWileyThe Scientific World Journal2356-61401537-744X2016-01-01201610.1155/2016/18716021871602The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical SystemYongjun Li0Xiaona Wei1Yanhong Zhang2School of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaSchool of Mathematics, Lanzhou City University, Lanzhou 730070, ChinaFirst, for a process U(t,τ)∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t)∣t≤T, for any T∈R, satisfying the following: (i) M(t) is compact, (ii) M(t) is positively invariant, that is, U(t,τ)M(τ)⊂M(t), and (iii) there exist k,l>0 such that dist(U(t,τ)B(τ),M(t))≤ke-(t-τ); that is, M(t) pullback exponential attracts B(τ). Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force.http://dx.doi.org/10.1155/2016/1871602 |
| spellingShingle | Yongjun Li Xiaona Wei Yanhong Zhang The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System The Scientific World Journal |
| title | The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System |
| title_full | The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System |
| title_fullStr | The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System |
| title_full_unstemmed | The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System |
| title_short | The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System |
| title_sort | existence of weak d pullback exponential attractor for nonautonomous dynamical system |
| url | http://dx.doi.org/10.1155/2016/1871602 |
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