Uniform attractors for multi-valued process generated by non-autonomous nonclassical diffusion equations with delay in unbounded domain without uniqueness of solutions

Article type: Research Article

Authors: Bai, Lihong^a | Zhang, Fanghong^{b; *}

Affiliations: [a] Department of Basic Courses, Gansu Institute of Architectural Technology, Lanzhou, China | [b] Department of Mathematics, Longqiao College of Lanzhou Commercial College, Lanzhou, China

Correspondence: [*] Corresponding author: Fanghong Zhang, Department of Mathematics, Longqiao College of Lanzhou Commercial College, Lanzhou, 730101, China. E-mail: [email protected].

Abstract: In this article, the existence of a uniform attractor is proved for the multi-valued process generated by non-autonomous nonclassical diffusion equations (NDEs) with delays in unbounded domain without uniqueness of solutions, when the external force g(x,t) belongs to the space LC∗2(R,L2(RN)) and is a translation bounded function, but is not a translation compact function.

Keywords: uniform attractors, multi-valued process, nonclassical diffusion equations with delay, unbounded domain

DOI: 10.3233/ASY-151299

Journal: Asymptotic Analysis, vol. 94, no. 3-4, pp. 187-210, 2015