A pulsar wind nebula inside a supernova remnant provides a unique insight into the properties of the central neutron star, the relativistic wind powered by its loss of rotational energy, its progenitor supernova, and the surrounding environment. In this paper, we present a new semi-analytic model for the evolution of such a pulsar wind nebula which couples the dynamical and radiative evolution of the pulsar wind nebulae, traces the evolution of the pulsar wind nebulae throughout the lifetime of the supernova remnant produced by the progenitor explosion, and predicts both the dynamical and radiative properties of the pulsar wind nebula during this period. We also discuss the expected evolution for a particular set of these parameters, and show it reproduces many puzzling features of known young and old pulsar wind nebulae. The model also predicts spectral features during different phases of its evolution detectable with new radio and gamma-ray observing facilities. Finally, this model has implications for determining if pulsar wind nebulae can explain the recent measurements of the cosmic ray positron fraction by PAMELA and the cosmic ray lepton spectrum by ATIC and HESS.
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