Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces

Article type: Research Article

Authors: Zhang, Jiangwei^a | Xie, Zhe^{b; *} | Xie, Yongqin^c

Affiliations: [a] College of Science, National University of Defense Technology, Changsha, China | [b] Research and Development Center, Sinoma Wind Power Blade Co., Ltd, Beijing, China | [c] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China

Correspondence: [*] Corresponding author. E-mail: xiezh@sinomatech.com.

Abstract: This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation parameter ν in Mt is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.

Keywords: Nonclassical diffusion equation, arbitrary polynomial growth, pullback attractor, memory, upper semi-continuity

DOI: 10.3233/ASY-231887

Journal: Asymptotic Analysis, vol. 137, no. 3-4, pp. 267-289, 2024