Then there exists a piecewise differentiable
adjoint variable .
The dynamics of the system are particularly interesting from a mathematical point of view as the model is described by a continuous two-dimensional piecewise differentiable
map characterized by several borders through which the system changes its definition.
So v([tau]) = u([tau]), u [less than or equal to] V, and V is a piecewise differentiable
and nondecreasing function and, by (16), it satisfies
Let us assume that in addition to conditions (1.4), the coefficient k = k([xi]) is piecewise differentiable and satisfies the condition
Let us assume that in addition to conditions of Theorem 2.1, the coefficient k([xi]) is piecewise differentiable and satisfies condition (4.6).
Because F is piecewise differentiable
, at this singularities, the Jacobian M will be replaced with the generalized Jacobian [delta]F .
where H(x) is a piecewise differentiable
nonstandard Heaviside function.