obtain the time dependence of bubble radius $R$ for each stage and duration of each stage. Also we will obtain conditions of steadiness of bubble growth for each stage.

Time Dependence of Bubble Radius
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Let us now solve the differential equations (\[Dyn-Eq-Henry\]) and (\[Dyn-Eq\]) for the time dependence of the bubble radius with the initial condition Eq. (\[R(0)\]) of homogeneous nucleation of the bubble. As it was in the previous section it is more convenient here to consider Henry’s and Sievert’s laws separately.

Henry’s Law
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At first we will rewrite Eq. (\[Dyn-Eq-Henry\]) in the form which is appropriate for integration: $$\label{For-Integration}
R \dot{R} + (R_\sigma + R_c) \dot{R} + (R_\sigma + R_c) R_c \frac{\dot{R}/R_c}{R/R_c - 1} = D s \zeta\; .$$ Integrating Eq. (\[For-Integration\]), we obtain $$\label{Integrated}
\frac{R^2}{2} + (R_\sigma + R_c) R + (R_\sigma + R_c) R_c \ln\left(\frac{R}{R_c} - 1\right) = D s \zeta \left(t + \tau \right)\; ,$$ where $\tau$ is the constant which has time dimensionality and which is defined by the initial value of radius at time $t=0$. Using initial condition (\[R(0)\]), from Eq. (\[Integrated\]) we find $$\label{tau}
\tau = \frac{2 R_c (R_\sigma + 2 R_c)}{D s \zeta}\; .$$ Excluding time $\tau$ from Eq. 