Abstract
AbstractIn this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters ν and the nonlinear term f satisfying the polynomial growth of arbitrary order $p-1$
p
−
1
($p \geq 2$
p
≥
2
). We extend the asymptotic a priori estimate method (see (Wang et al. in Appl. Math. Comput. 240:51–61, 2014)) to verify asymptotic compactness and upper semicontinuity of a family of semigroups for autonomous dynamical systems (see Theorems 2.2 and 2.3). By using the new operator decomposition method, we construct asymptotic contractive function and obtain the upper semicontinuity for our problem, which generalizes the results obtained in (Wang et al. in Appl. Math. Comput. 240:51–61, 2014). In particular, the regularity of global attractors is obtained, which extends and improves some results in (Xie et al. in J. Funct. Spaces 2016:5340489, 2016; Xie et al. in Nonlinear Anal. 31:23–37, 2016).
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference33 articles.
1. Wang, L., Wang, Y., Qin, Y.: Upper semicontinuity of attractors for nonclassical diffusion equations in $H^{1}(\mathbb{R}^{3})$. Appl. Math. Comput. 240, 51–61 (2014)
2. Xie, Y., Li, Y., Zeng, Y.: Uniform attractors for nonclassical diffusion equations with memory. J. Funct. Spaces 2016, Article ID 5340489 (2016)
3. Xie, Y., Li, Q., Zhu, K.: Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity. Nonlinear Anal. 31, 23–37 (2016)
4. Aifantis, E.C.: On the problem of diffusion in solids. Acta Mech. 37, 265–296 (1980)
5. Barenblatt, G., Zheltov, I.P., Kochina, I.N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. 24, 1286–1303 (1960)
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献