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Attractors for the nonclassical diffusion equations with fading memory |
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| Authors: | Xuan Wang Lu Yang Chengkui Zhong |
| Affiliation: | aCollege of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China;bSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China;cDepartment of Mathematics, Nanjing University, Nanjing, 210093, China |
| Abstract: | We discuss long-time dynamical behavior of the nonclassical diffusion equation with fading memory when nonlinearity is critical. The existence and regularity of global attractors in weak topological space and strong topological space are obtained, while the forcing term only belongs to H−1(Ω) and L2(Ω) respectively. The results in this part are new and appear to be optimal corresponding to the forcing term. |
| Keywords: | Nonclassical diffusion equation Global attractor Critical exponent Fading memory |
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