[FORTHCOMING] Comportement à long terme d’une classe d’équations paraboliques non-locales sans unicité

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