Premium
Well‐posedness of a parabolic free boundary problem driven by diffusion and surface tension
Author(s) -
Zaal Martijn M.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3076
Subject(s) - mathematics , uniqueness , free boundary problem , mathematical analysis , boundary (topology) , sobolev space , boundary value problem , curvature , mixed boundary condition , robin boundary condition , diffusion , domain (mathematical analysis) , mean curvature , geometry , physics , thermodynamics
Well‐posedness and regularity results are shown for a class of free boundary problems consisting of diffusion on a free domain where the boundary movement depends on its mean curvature of the boundary and the diffusion on the boundary, and initial conditions are radially symmetric. Short‐time existence and uniqueness of solutions in a suitable Sobolev space are shown using a fixed‐point argument. Higher regularity is a posteriori. Finally, it is shown that solutions exist globally in time and converge to equilibrium if the boundary movement depends on the mean curvature of the boundary and diffusion in a specific way. A mathematical model describing the swelling of a cell due to osmosis is treated as an example. Copyright © 2014 John Wiley & Sons, Ltd.