Sentence examples for generate an evolution from inspiring English sources

Then the (A t)) generate an evolution family ((U t, s))_{tgeq s}) such that U t, s)v xi) = T(t -s e^{int_{s}^{t} -2+sintau+sinpitau ),dtau} -2+sintau+sinpitau

Consequently, (A t)) generates an evolution operator (S t,S t.

Then generates an evolution operator satisfying assumptions (see [23]).

It is assumed also that -A t,.) generates an evolution operator in the Banach space X.

Then it is not difficult to verify that generates an evolution operator satisfying assumptions and (5.9).

Then (A t)) generates an evolution operator and (R t,s)) can be reduced by this evolution operator such that ((A_{1})) is satisfied (see [26] for details).

where A ( t ) is a family of linear operators which generates an evolution system { U ( t, s ) : 0 ≤ s ≤ t ≤ b }.

(1.1) where (A t)) is a family of linear operators which generates an evolution system ({U t,s): 0leq sleq tleq b}).

On the other hand, assuming that condition (A) holds, (A cdot)) generates an evolution operator (S t, s)) which satisfies S t,s) z = S_{0}(t -s) z + int_{s}^{t} S_{0}(t - tau) B tau) S( tau, s) z,dtau.

Henceforth in this text, we will assume that A generates an evolution operator S, in the sense introduced in Kozak [11], Definition 2.1 (see also Henríquez [21], Definition 1.1).

Moreover, we assume that (b : [0, infty) tomathbb{R}) is a continuously differentiable function such that (b t) geq1) for all (t geq0). We consider the operator (A t) = b t) A_{0} ) with domain (D(A t)) = D(A_{0})). Initially we will show that (A t)) generates an evolution operator (S t,S t.