On stability of solutions to the Cauchy problem for hyperbolic systems in two independent variables

Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

“…From (15) and (16) we derive W (τ + T, τ ) ≤ q. It follows from (14) that W (τ + nT, τ ) = [W (τ + T, τ )] n , n = 0, 1, 2, . .…”

“…In Section 1 we represent some facts about this operator from [14] in a form convenient for the sequel.…”

“…The shift operator along the characteristics of the system which was introduced in [14] and enabled us to reduce the Cauchy problem for a hyperbolic system to the Cauchy problem for an ordinary differential equation with a bounded operator coefficient in a Hilbert space is used here in a somewhat different way. In Section 1 we represent some facts about this operator from [14] in a form convenient for the sequel.…”

“…The stability of solutions to the Cauchy problem and the mixed problem of the indicated type for a hyperbolic system with one spatial variable was addressed by the direct Lyapunov method in [14][15][16]. Some sufficient conditions were established for asymptotic stability in various norms.…”