Abstract

In this article, we investigate the long-time behavior for the ill-posed problems 2ut2+ut+λuΔuΔutΔ2ut2=f(t,u(x,tρ(t)))+g(t,x),in(τ,+)×RN, with some hereditary characteristics. First, we establish the existence of solutions for the second-order non-autonomous evolution equation by the standard Faedo-Galerkin methods, but without any Lipschitz conditions on the nonlinear term f(). Then, by proving the D-pullback asymptotically upper-semicompact property for the multivalued process {U(t,τ)}, we establish the existence of pullback attractors ACH1(RN),H1(RN) in the Banach spaces CH1(RN),H1(RN) for the multi-valued process generated by a class of second-order non-autonomous evolution equations with delays and ill-posedness.

Details

Title
Pullback attractors for a class of second-order delay evolution equations with dispersive and dissipative terms on unbounded domain
Author
Fang-hong, Zhang 1 

 Regional Circular Economy key Laboratory of Gansu Higher Institutions, Lanzhou, P. R. China; Department of Mathematics, Lanzhou Technology and Business College, Lanzhou, P. R. China 
Publication year
2025
Publication date
2025
Publisher
De Gruyter Poland
e-ISSN
23915455
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3215090439
Copyright
© 2025. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.