The uncertain functional differential equation (UFDE) is a type of functional differential equations driven by a canonical uncertain process. Uncertain functional differential equation with infinite delay (IUFDE) have been widely applied in sciences and technology. In this paper, we prove an existence and uniqueness theorem for IUFDE intheinterval [t0, T][t0, T], underuniform Lipschitz condition and weak condition. Also, the novel existence and uniqueness theorem under the linear growth condition and the local Lipschitz condition is proven. In the following, a more general type of UFDE considers, which the future state is determined by entire of the past states rather than some of them. Finally, the existence and uniqueness theorem is considered on theinterval [t0, ∞ ].

In this paper, we consider a Cahn-Hilliard/Allen-Cahn equation. By using the semigroups and the classical existence theorem of global attractors, we give the existence of the global attractor in Hk (0£k<5) space of this equation, and it attracts any bounded subset of Hk(W) in the Hk -norm.

In this paper, we prove the existence of weak global solutions for a class of generic reaction diffusion systems for which two main properties hold: the quasi-positivity and a triangular structure condition on the nonlinearities. The main result is a generalization of the work already done on models of a single reaction-diffusion equation. The model studied is applied in image recovery and contrast enhancement. It can also be applied to many models in biology and radiology.