Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Xiaolei Dong; Yuming Qin; Xiaolei Dong; Yuming Qin

doi:10.3934/math.2022449

AIMS Mathematics

2022, Volume 7, Issue 5: 8064-8079. doi: 10.3934/math.2022449

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Research article

Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Xiaolei Dong ¹,
Yuming Qin ^{2,3
,
,}

1.
College of Information Science and Technology, Donghua University, Shanghai 201620, China
2.
Department of Mathematics, Donghua University, Shanghai 201620, China
3.
Institute for Nonlinear Science, Donghua University, Shanghai 201620, China

Received: 08 January 2022 Revised: 11 February 2022 Accepted: 17 February 2022 Published: 24 February 2022
MSC : 35B40, 35B41, 35K57, 37F10

In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $. First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by ^[6], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $.
- nonclassical diffusion equations,
- finite fractal dimension,
- pullback attractors
Citation: Xiaolei Dong, Yuming Qin. Finite fractal dimension of pullback attractors for a nonclassical diffusion equation[J]. AIMS Mathematics, 2022, 7(5): 8064-8079. doi: 10.3934/math.2022449

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Abstract

In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $. First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by ^[6], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $.

References

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