  We study the evolution of one-dimensional relativistic jets, using the exact
solution of the Riemann problem for relativistic flows. For this purpose, we
solve equations for the ideal special relativistic fluid composed of dissimilar
particles in flat space-time and the thermodynamics of fluid is governed by a
relativistic equation of state. We obtain the exact solution of jets impinging
on denser ambient media. The time variation of the cross-section of the
jet-head is modeled and incorporated. We present the initial condition that
gives rise to a reverse shock. If the jet-head cross-section increases in time,
the jet propagation speed slows down significantly and the reverse-shock may
recede opposite to the propagation direction of the jet. We show that the
composition of jet and ambient medium can affect the jet solution
significantly. For instance, the propagation speed depends on the composition
and is maximum for a pair-dominated jet, rather than a pure electron-positron
or electron-proton jet. The propagation direction of the reverse-shock may also
strongly depend on the composition of the jet.
