  Spherically symmetric time-dependent solutions for the 5D system of a scalar
field canonically coupled to gravity are obtained and identified as an
extension of recent results obtained by Ahmed, Grzadkowskia and Wudkab. The
corresponding cosmology of models with regularized branes generated by such a
5D scalar field scenario is also investigated. It has been shown that the
anisotropic evolution of the warp factor and consequently the Hubble like
parameter are both driven by the radial coordinate on the brane, which leads to
an emergent thick brane-world scenario with spherically symmetric time
dependent warp factor. Meanwhile, the separability of variables depending on
fifth dimension, y, which is exhibited by the equations of motion, allows one
to recover the extra dimensional profiles obtained in the literature, namely
the extra dimensional part of the scale (warp) factor and the scalar field
dependence on y. Therefore, our results are mainly concerned with the time
dependence of a spherically symmetric warp factor. Besides evincing
possibilities for obtaining asymmetric stable brane-world scenarios, the extra
dimensional profiles here obtained can also be reduced to those ones
investigated in the literature.
