"[Social networks like Twitter and Facebook] have a very unique problem, in that all these audiences are very disaggregated.
It is easy to prove that the problem (1.1 - 1.6 1.1 - 1.6ique local-in-time strong solution [6, 9], and thas we omit the details here.
Since it is easy to prove that problem (1.1 - 1.5) has a unique local-in-time strong solution, we omit the details.
Remark 1.3 When the space dimension n = 2, we can prove that the problem (1.1 - 1.6 1.1 - 1.6ique global-in-time strong solution by thassame method as that in [10], and thuniqueomit the details here.
On the condition that (47). the given problem has a unique solution in the space.
Thus, by using Theorem 2.2, the problem has a unique solution in P h = P 1.
It follows from ([15] and [13]) that initial boundary value problem has a unique solution in appropriate Sobolev space of negative order.
If this solvability condition is fulfilled, then the Zaremba problem has a unique solution in the space R E 1, p ( D a, γ, δ, σ S + w ) Open image in new window.
Under this condition, the problem has a unique solution in R E 1, p ( D, σ S + w ) Open image in new window given by u = u s + c with u s ( z ) = R ∫ z 0 z ( ln c - 1 ( z ′ ) ) ′ σ S + ( c - 1 ( z ′ ) ) × ∫ T u 0, 1 ( c | c ′ | σ S - 1 π ı 1 ζ - c - 1 ( z ′ ) d ζ d z ′ Open image in new window.
then (1) For the Zaremba problem to possess a solution in R E 1, p ( D a, γ, δ, σ S + w ) Open image in new window, it is necessary and sufficient that 1 π ı ∫ T U 0, 1 | c a, γ, δ ′ | σ S - d ζ ζ = 0. Open image in new window (2) If this solvability condition is fulfilled, then the Zaremba problem has a unique solution in the space R E 1, p ( D a, γ, δ, σ S + w ) Open image in new window.
