PULLBACK EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS ABSTRACT RETARDED EVOLUTION EQUATIONS

Jinying Wei; Yongjun Li

doi:10.11948/20210415

2022 Volume 12 Issue 4

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Jinying Wei, Yongjun Li. PULLBACK EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS ABSTRACT RETARDED EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1595-1612. doi: 10.11948/20210415

Citation:

Jinying Wei, Yongjun Li. PULLBACK EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS ABSTRACT RETARDED EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1595-1612. doi: 10.11948/20210415

PULLBACK EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS ABSTRACT RETARDED EVOLUTION EQUATIONS

Jinying Wei^1, ,,
Yongjun Li¹

1.
School of Mathematics, Lanzhou City University, No.11, Jiefang Road, 730070, China

Corresponding author: Email: weijy2818@163.com(J. Wei)
Fund Project: The authors were supported by NNSF of China(No. 11761044) and Youth Doctoral Foundation of Gansu Education Commitee(No. 2021QB-117)

Abstract

Abstract

In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space $ H $:

$ u'(t)+ Au(t)=F(t,\,u(t),\,u(t-r_1),\ldots,\,u(t-r_n)), $

where $ A: D(A)\subset H\rightarrow H $ is a positive definite selfadjoint operator with compact resolvent, and $ F: {\mathbb{R}}\times D(A^{\alpha})^{n+1}\rightarrow H(\alpha \in [0,\,1/2]) $ is a locally Lipschitz continuous mapping. We slightly generalize a theoretical existence result for pullback exponential attractors. Based on our abstract theorem, we prove some existence results of pullback exponential attractor for this delay differential equations and derive estimates on the fractal dimension of the attractors.
- Pullback exponential attractor /
- retarded evolution equation /
- delay /
- fractal dimension
MSC: 37L30, 37B55, 35B41, 34D45, 37L25

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References

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