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- Title
Upper semicontinuity of uniform attractors for nonclassical diffusion equations.
- Authors
Wang, Yonghai; Li, Pengrui; Qin, Yuming
- Abstract
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\in \Sigma $ ) attractor $\mathcal {A}^{\varepsilon }_{\Sigma }$ ( $\varepsilon \geqslant 0$ ) for equation (1.1) satisfies $\lim_{\varepsilon \to \varepsilon _{0}}\operatorname{dist}_{H_{0}^{1}(\Omega )}(\mathcal {A}^{\varepsilon } _{\Sigma },\mathcal {A}^{\varepsilon _{0}}_{\Sigma })=0$ for any $\varepsilon _{0}\geqslant 0$ .
- Subjects
ATTRACTORS (Mathematics); BURGERS' equation; HEAT equation; UNIFORM algebras; OPERATOR algebras
- Publication
Boundary Value Problems, 2017, Vol 2017, Issue 1, p1
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-017-0816-7