The solution of the equation is φt, and since it is the solution of differential equation it is differentiable.
It is differentiable if the derivative exists for all t for which f(t) is defined.
f is differentiable if it is differentiable at every point of M1.
Further, we say that X is (i -differentiable or (i -differentiablee or [ a, b ], ii -differentiableii -differentiable (i) on (ii) of Definition 2.2, respectively.
Moreover, it is straightforwardly differentiable when considering that compactified [0, 1 -fluxes are continuous and smooth in the [0, ∞)-flux space and vice versa.
Note that when is differentiable on some open set containing, then, since is lower semicontinuous proper convex, the generalized variational inequality (GVI) is equivalent to the following variational inequalities (see [25, 26]): Find such that (2.5).
In practice, when ( f) is differentiable and the computation of its gradient is not difficult, and the projection on (C) can be inexpensively determined, the use of DCAP2 is very recommended.
It is clear that is differentiable at any and.
Although the derivative does not exist "in the interfacial regions, (phi) moves swiftly to approximate its equilibrium profile (in the same manner as when A is differentiable)"—Taylor and Cahn (1998).
In addition, (D_{q,omega}f omega_{0})=f' omega_{0})) when f is differentiable at (omega_{0}).
