1. 2. 1. 2. Pullback attractors for a class of non-autonomous nonclassical diffusion equations Anh C.T., Bao T.Q. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam Abstract: We consider the first initial boundary value problem for the non-autonomous nonclassical diffusion equation ut-εΔu t-Δu+f(u)=g(t), ε[0,1], in a bounded domain in n. Under a Sobolev growth rate of the nonlinearity f and a suitable exponential growth of the external force g, using the asymptotic a priori estimate method, we prove the existence of pullback D-attractors si;̂ in the space H01(Ω) and the upper semicontinuity of Aε̂ at ε=0. © 2010 Elsevier Ltd. All rights reserved. Author Keywords: A priori estimate method; Compactness method; Global solution; Non-autonomous nonclassical diffusion equation; Pullback attractor; Upper semicontinuity Index Keywords: A-priori estimates; Diffusion equations; Global solutions; Nonautonomous; Upper semi- continuity; Diffusion; Dynamical systems; Partial differential equations; Sobolev spaces; Control nonlinearities Year: 2010 Source title: Nonlinear Analysis, Theory, Methods and Applications Volume: 73 Issue: 2 Page : 399-412 Link: Scorpus Link Correspondence Address: Anh, C. T.; Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam; email: anhctmath@hnue.edu.vn ISSN: 0362546X CODEN: NOAND DOI: 10.1016/j.na.2010.03.031 Language of Original Document: English Abbreviated Source Title: Nonlinear Analysis, Theory, Methods and Applications Document Type: Article Source: Scopus Authors with affiliations: Anh, C.T., Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam Bao, T.Q., Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam References: Aifantis, E.C., On the problem of diffusion in solids (1980) Acta Mech., 37, pp. 265-296 Peter, J.C., Gurtin, M.E., On a theory of heat conduction involving two temperatures (1968) Z. Angew. Math. Phys., 19, pp. 614-627