  We study analytically the process of a topological texture collapse in the
approximation of a scaling ansatz in the nonlinear sigma-model. In this
approximation we show that in flat space-time topological texture eventually
collapses while in the case of spatially flat expanding universe its fate
depends on the rate of expansion. If the universe is inflationary, then there
is a possibility that texture will expand eternally; in the case of exponential
inflation the texture may also shrink or expand eternally to a finite limiting
size, although this behavior is degenerate. In the case of power law
noninflationary expansion topological texture eventually collapses. In a cold
matter dominated universe we find that texture which is formed comoving with
the universe expansion starts collapsing when its spatial size becomes
comparable to the Hubble size, which result is in agreement with the previous
considerations. In the nonlinear sigma-model approximation we consider also the
final stage of the collapsing ellipsoidal topological texture. We show that
during collapse of such a texture at least two of its principal dimensions
shrink to zero in a similar way, so that their ratio remains finite. The third
dimension may remain finite (collapse of cigar type), or it may also shrink to
zero similar to the other two dimensions (collapse of scaling type), or shrink
to zero similar to the product of the remaining two dimensions (collapse of
pancake type).
