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 $$\{\varepsilon_n\}_{n \in \mathbb{N}}$$ , $$\varepsilon_n>0$$ . 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 $$\{\varepsilon\}$$ , $$\varepsilon>0$$ .