  The phase dynamics of a long Josephson junction with spatially
inhomogeneously distributed bias current is considered for the case of a dense
soliton chain (regime of the Flux Flow oscillator). To derive the analytical
solution of the corresponding sine-Gordon equation the Poincare method has been
used. In the range of the validity of the theory good coincidence between
analytically derived and numerically computed current-voltage characteristics
have been demonstrated for the simplest example of unitstep function
distribution of bias current (unbiased tail). It is shown, that for the
considered example of bias current distribution, there is an optimal length of
unbiased tail that maximizes the amplitude of the main harmonic and minimizes
the dynamical resistance (thus leading to reduction of a linewidth).
