Convergence to a self similar solution of a one-dimensional one-phase Stefan Problem

Meriem Bouguezzi (1, 2) , Danielle Hilhorst (1, 3) , Yasuhito Miyamoto (4) , Jean-Francois Scheid (5, 6)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 CNRS - Centre National de la Recherche Scientifique
4 Tokyo University of Science [Tokyo]
5 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
6 IECL - Institut Élie Cartan de Lorraine

We revisit the one-dimensional one-phase Stefan problem with a Dirichlet boundary condition at x = 0 as stated in the book of Avner Friedman about parabolic equations [F3]. We prove that under rather general hypotheses on the initial data, the solution converges to a self-similar profile as t → +∞.

Mots clés: 2010 Mathematics Subject Classification: Primary 35R35; 35C06; 35B40; Secondary 80A22 Stefan problem; free-boundary problem; self-similar solution; large-time behavior

Domaines: Equations aux dérivées partielles [math.AP]

Meriem Bouguezzi, Danielle Hilhorst, Yasuhito Miyamoto, Jean-Francois Scheid. Convergence to a self similar solution of a one-dimensional one-phase Stefan Problem. 2020. ⟨hal-03090682⟩