By the classical theory concerning the existence and uniqueness of the solutions of evolution differential equations (cf. [15]), we have the following lemma (see [23] for details).
We discuss the use of numerical methods in the study of the solutions of evolution problems which exhibit finite-time unbounded growth.
We discuss in this article the application of controllability techniques to the computation of the time-periodic solutions of evolution equations.
On the other hand, the existence of periodic solutions or almost periodic solutions of evolution equations has been investigated by many authors (cf., e.g., [2, 4, 5, 9 11, 14, 15, 17 19, 24]).
By the classical semigroup theory of existence and uniqueness of solutions of evolution differential equations [20], the random partial differential equation (3.4) has a unique solution in the mild sense varphi t,omega)=e^{L t-tau)}varphi(tau,omega)+int_{tau}^{t}e^{L t-tauFbigl(varphi(s),omegabigr), ds for any (varphi(tau,omega)in E).
For the Cauchy problems the topological structure of the solution set of evolution inclusions was examined primarily by Papageorgiou and Shahzad [10], Andres and Pavlǎcková [11], Chen et al. [12] and Papageorgiou and Yannakakis [13] in a Banach space.
For Cauchy problems the topological structure of the solution set of evolution inclusions was examined by Bothe [23], Andres-Pavlackova [24], Gabor-Grudzka [25], and Chen-Wang-Zhou [26] in a Banach space, Bakowska-Gabor [27], and O'Regan [28] in Fréchet spaces.
Jin and Yang in [4] established the existence and uniqueness of a weak solution for the associated evolution equations of the JY model, and showed that the solution of the evolution equation converges weakly in BV and strongly in L 2 to the minimizer as t → ∞.
In this paper, we have studied the existence and uniqueness of a solution of the evolution equation for a smooth neural mass model called the structure tensor model.
