ON THE UNIQUENESS OF THE CLASSICAL SOLUTION OF THE FINGERING PROBLEM IN A HELE-SHAW CELL WITH SURFACE TENSION

The existence of a classical solution was established for a one-phase radial viscous fingering problem in a Hele-Shaw cell under surface tension (original problem) by means of parabolic regularization for a certain subsequence \(\{\varepsilon_n\}_{n \in \mathbb{N}}\) $\{{\epsilon }_n{\}}_{n\in \mathbb{N}}$ , \(\varepsilon_n>0\) ${\epsilon }_n>0$ . In this paper, we prove the uniqueness of the classical solution to the original problem with the use of parabolic regularization for the full sequence of the parameter \(\{\varepsilon\}\) $\left\{\epsilon \right\}$ , \(\varepsilon>0\) $\epsilon >0$ .