  The model of a signature change of a metric from the Lorenztian to Euclidean
one with the use of a time dependent kink as $g_{00}$ component of the metric
is considered. The metric which describes the continuous change of the
signature of this type on a hypersurface is constructed and corresponding
Einstein equations are solved in both regions of the space-time. The
discontinuities of the Einstein tensor components on the hypersurface are
discussed as well as junction conditions for the parameters of the solutions.
Additionally, the properties of a transition from the space-time with one
signature to an another are discussed, the presence of an inflation in the
model is demonstrated as a consequence of the signature change without any
additional fields required.
