2018/10/24 by Augner, Björn, Laasri, Hafida
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1810.10271
We study the non-autonomous version of an infinite-dimensional port-Hamiltonian system on an interval [a, b]. Employing abstract results on evolution families, we show C1-well-posedness of the corresponding Cauchy problem, and thereby existence and uniqueness of classical solutions for sufficiently regular initial data. Further, we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay of the energy in this non-autonomous setting.