Attractors and asymptotic regularity for nonclassical diffusion equations in locally uniform spaces with critical exponent

Uniform attractors of nonclassical diffusion equations on ℝN with memory and singularly oscillating external forces

“…In the last two decades, many researchers have concentrated on the theory of attractors for dynamical systems. The existence and long-time behavior of solutions to nonclassical diffusion equations have been investigated extensively in various cases, such as in the cases of autonomous (see other works [5][6][7][8][9][10][11] ) and of nonautonomous (see other studies 7,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], and even in the case with finite delay (see other works [21][22][23] ). Besides, these equations with singularly oscillating external force have been also studied in Anh and Toan, 24 where they obtained the boundedness and the upper semicontinuity of uniform attractors in the case when the domain is unbounded and the nonlinearity is of Sobolev type.…”