On a Dissolution-Growth Problem with Surface Tension in the Neighborhood of a Stationary Solution
Frédéric Abergel, Danielle Hilhorst, Françoise Issard‐Roch · SIAM Journal on Mathematical Analysis · 1993
The authors consider a one-phase Stefan problem with surface tension in dimension two and show a well-posedness result in the neighborhood of a stationary solution, in the case that the moving interface is parametrized in the form $y = f(x,t)$.