Powered swing-by in the elliptic restricted three-body problem

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“…w(t, 0) = ψ 2 (t), t ∈ [0, T ]. (11) Here the functions F (t, x) ∈ C(Ω, R n ). Let t 0 = 0, t m+1 = T .…”

“…The problems (9)- (11) and 12- (16) are equivalent in the following sense. If the function w(t, x) is a classical solution to (9)- (11), then system of pairs (λ r (x), w r (t, x)), where λ r (x) = w(t r−1 , x) and w r (t, x) = w(t, x) − w(t r−1 , x), and (t, x) ∈ Ω r , and r = 1, m + 1 is a solution to problem (12)- (16).…”

“…The problems (9)- (11) and 12- (16) are equivalent in the following sense. If the function w(t, x) is a classical solution to (9)- (11), then system of pairs (λ r (x), w r (t, x)), where λ r (x) = w(t r−1 , x) and w r (t, x) = w(t, x) − w(t r−1 , x), and (t, x) ∈ Ω r , and r = 1, m + 1 is a solution to problem (12)- (16). Conversely, if the system of pairs (λ * r (x), w * r (t, x)), (t, x) ∈ Ω r , and r = 1, m + 1, is a solution to (12)- (16), then the function w * (t, x) defined by the equalities w * (t, x) = λ * r (x) + w * r (t, x) for all (t, x) ∈ Ω r , and r = 1, m + 1, is a classical solution to problem (9)- (11).…”

“…Then nonlocal problem for system of loaded hyperbolic equations of the second order (9)- (11) has unique classical solution.…”

“…Many problems of dynamics and kinetics of gas sorption, processes of drying by air stream, movement of adsorbed mixtures and others lead to the study of nonlocal problems for the systems of hyperbolic equations with loading [1][2][3][4][5][6][7][8][9][10] and also for nonlocal problems with integral conditions for equations of hyperbolic type [11][12][13][14][15][16]. In order to solve these problems, the theoretical methods of ordinary differential equations, loaded differential equations, numerical-analytical method are applied, and new approaches and methods are developed as well.…”