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On the dynamics of a class of nonclassical parabolic equations
Authors:Suyun Wang  Desheng Li  Chengkui Zhong
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
Abstract:We consider the first initial and boundary value problem of nonclassical parabolic equations utμΔutΔu+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 View the MathML source in the topology of H2(Ω); moreover, AμA0 in the sense of Hausdorff semidistance in View the MathML source as μ goes to 0.
Keywords:Nonclassical parabolic equation  Singular point  Uniform decay estimate  Global attractor  Upper-continuity
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