  The theory describing the evolution of inhomogeneous vortex tangle at zero
temperature is developed on the bases of kinetics of merging and splitting
vortex loops. Vortex loops composing the vortex tangle can move as a whole with
some drift velocity depending on their structure and their length. The flux of
length, energy, momentum etc. executed by the moving vortex loops takes a
place. Situation here is exactly the same as in usual classical kinetic theory
with the difference that the "carriers" of various physical quantities are not
the point particles, but extended objects (vortex loops), which possess an
infinite number of degrees of freedom with very involved dynamics. We offer to
fulfill investigation basing on supposition that vortex loops have a Brownian
structure with the only degree of freedom, namely, lengths of loops $l$. This
conception allows us to study dynamics of the vortex tangle on the basis of the
kinetic equation for the distribution function $n(l,t)$ of the density of a
loop in the space of their lengths. Imposing the coordinate dependence on the
distribution function $n(l,\mathbf{% r},t)$ and modifying the "kinetic"
equation with regard to inhomogeneous situation, we are able to investigate
various problem on the transport processes in superfluid turbulence. In this
paper we derive relation for the flux of the vortex line density
$\mathcal{L}(x,t)$. The correspoding evolution of quantity $\mathcal{L}(x,t)$
obeys the diffusion type equation as it can be expected from dimensional
analysis. The according diffusion coefficient is evaluated from calculation of
the (size dependent) free path of the vortex loops. We use this equation to
describe the decay of the vortex tangle at very low temperature. We compare
that solution with recent experiments on decay of the superfluid turbulence.
