Upper semicontinuity of uniform attractors for nonclassical diffusion equations

We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.) g ∈ Σ ) attractor A Σ ε ( ε ⩾ 0 ) for equation ( 1.1 ) satisfies lim ε → ε 0 dist H 0 1 ( Ω ) (...

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Bibliographic Details
Published in:Boundary value problems 2017-06, Vol.2017 (1), p.1-11, Article 84
Main Authors: Wang, Yonghai, Li, Pengrui, Qin, Yuming
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Difference and Functional Equations
Mathematical analysis
Mathematics
Mathematics and Statistics
nonautonomous
nonclassical diffusion equation
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
uniform attractor
upper semicontinuity
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Summary:We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.) g ∈ Σ ) attractor A Σ ε ( ε ⩾ 0 ) for equation ( 1.1 ) satisfies lim ε → ε 0 dist H 0 1 ( Ω ) ( A Σ ε , A Σ ε 0 ) = 0 for any ε 0 ⩾ 0 .
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-017-0816-7