Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 1 (January 2025) > Article
Le Tran Tinh
Hong Duc University
Vietnam
Published on 20 January 2025 DOI : 10.21494/ISTE.OP.2025.1256
In this paper we consider a class of nonlocal parabolic equations without uniqueness using a new framework developed by Cheskidov and Lu which called evolutionary system. We first prove the existence of weak solutions by using the compactness method. However, the Cauchy problem can be non-unique and we also give a sufficient condition for uniqueness. Then we use the theory of evolutionary system to investigate the asymptotic behavior of weak solutions via attractors and its properties. The novelty is that our results extend and improve the previous results and it seems to be the first results for this kind of system via using evolutionary systems.
In this paper we consider a class of nonlocal parabolic equations without uniqueness using a new framework developed by Cheskidov and Lu which called evolutionary system. We first prove the existence of weak solutions by using the compactness method. However, the Cauchy problem can be non-unique and we also give a sufficient condition for uniqueness. Then we use the theory of evolutionary system to investigate the asymptotic behavior of weak solutions via attractors and its properties. The novelty is that our results extend and improve the previous results and it seems to be the first results for this kind of system via using evolutionary systems.
evolutionary systems global attractors trajectory attractors nonlocal parabolic equations normal functions translation bounded functions tracking properties
evolutionary systems global attractors trajectory attractors nonlocal parabolic equations normal functions translation bounded functions tracking properties