On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularization
Yuri Evgenyevich Hohlov, Michael Reissig · European Journal of Applied Mathematics · 1995
In this paper, Hele-Shaw moving boundary problems with kinetic undercooling regularization are studied. By application of the nonlinear abstract Cauchy–Kovalevskaya theorem the local existence of analytic solutions is shown. Therefore we have to study the behaviour of the gradient of harmonic functions up to the boundary of the domain.