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We study the non-autonomous version of an infinite-dimensionalport-Hamiltonian system on an interval $[a, b]$. Employing abstract results onevolution families, we show $C^1$-well-posedness of the corresponding Cauchyproblem, and thereby existence and uniqueness of classical solutions forsufficiently regular initial data. Further, we demonstrate that a dissipationcondition in the style of the dissipation condition sufficient for uniformexponential stability in the autonomous case also leads to a uniformexponential decay of the energy in this non-autonomous setting.

Exponential stability for infinite-dimensional non-autonomous port-Hamiltonian Systems