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Uniform attractors of nonclassical diffusion equations on ℝ N with memory and singularly oscillating external forces
Author(s) -
Le Thi Thuy,
Nguyen Duong Toan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6791
Subject(s) - mathematics , attractor , class (philosophy) , kernel (algebra) , nonlinear system , mathematical analysis , convergence (economics) , diffusion , uniform boundedness , pure mathematics , bounded function , physics , quantum mechanics , artificial intelligence , computer science , economics , economic growth
In this paper, we consider a class of nonclassical diffusion equations onℝ Nwith hereditary memory, in presence of singularly oscillating external forces depending on a positive parameter ε and a new class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. Under a general assumption on the memory kernel κ and for a very large class of nonlinearities, we prove the existence of uniform attractors inH 1 ( ℝ N ) × L μ 2 ( ℝ + , H 1 ( ℝ N ) ) . The uniform boundedness (w.r.t. ε ) and the convergence of uniform attractorsA εas ε tends to 0 are also studied. Our results extend and improve some results in Anh and Toan.