On the dynamics of a class of nonclassical parabolic equations |
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Authors: | Suyun Wang Desheng Li Chengkui Zhong |
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Institution: | a Department of Mathematics, Lanzhou Teachers College, Lanzhou 730070, Gansu, PR China b Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, PR China c Department of Mathematics, Lanzhou University, Lanzhou 730000, PR China |
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Abstract: | We consider the first initial and boundary value problem of nonclassical parabolic equations ut−μΔut−Δu+g(u)=f(x) on a bounded domain Ω, where μ∈0,1]. First, we establish some uniform decay estimates for the solutions of the problem which are independent of the parameter μ. Then we prove the continuity of solutions as μ→0. Finally we show that the problem has a unique global attractor Aμ in in the topology of H2(Ω); moreover, Aμ→A0 in the sense of Hausdorff semidistance in as μ goes to 0. |
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Keywords: | Nonclassical parabolic equation Singular point Uniform decay estimate Global attractor Upper-continuity |
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