The asymptotic behavior of solutions to the Cauchy problem for Vlasov-Poisson and Vlasov-Maxwell systems is examined in one space dimension. Both monocharged and neutral systems are studied in the classical and relativistic contexts. A new identity yields spacetime integrability of certain positive quantities from which various modes of time decay may be deduced. From other estimates one finds rates of the growth of the momentum support when the initial data have compact support.
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