Research article

Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

  • 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) $.

    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

    Related Papers:

  • 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) $.



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