On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularization

1995 ◽  
Vol 6 (5) ◽  
pp. 421-439 ◽  
Author(s):  
Yu. E. Hohlov ◽  
M. Reissig
Keyword(s):  
Harmonic Functions ◽  
Moving Boundary ◽  
Local Existence ◽  
Analytic Solutions ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
Classical Solvability ◽  
Kinetic Undercooling

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.

Complex variable methods in Hele–Shaw moving boundary problems

1992 ◽  
Vol 3 (3) ◽  
pp. 209-224 ◽  
Author(s):  
S. D. Howison
Keyword(s):  
Surface Tension ◽  
Moving Boundary ◽  
Moving Boundary Problems ◽  
Schwarz Function ◽  
Boundary Problems ◽  
Kinetic Undercooling ◽  
Ill Posed ◽  
Two Space Dimensions ◽  
New Interpretation ◽  
The One

We discuss the one-phase Hele–Shaw problem in two space dimensions. We review exact solutions in the zero-surface-tension case, giving a unified account of the Schwarz function and conformal mapping approaches. We discuss the extension of the former method to the cases in which surface tension or ‘kinetic undercooling’ terms apply on the moving boundary, and we give some conjectures on the resulting singularity structure. Finally, we give a new interpretation of the linear stability analysis of the zero-surface-tension problem, and we suggest a possible regularization of ill-posed problems by the imposition of a unilateral constraint on the moving boundary.

USNCCM-11: Computational fluid mechanics for free and moving boundary problems

2013 ◽  
Vol 87 ◽  
pp. 1
Author(s):  
Rekha R. Rao ◽  
S.A. Roberts ◽  
David R. Noble ◽  
Patrick D. Anderson ◽  
Jean-Francois Hétu
Keyword(s):  
Fluid Mechanics ◽  
Moving Boundary ◽  
Computational Fluid Mechanics ◽  
Moving Boundary Problems ◽  
Boundary Problems

Solving moving boundary problems with an adaptive moving grid method

1998 ◽  
Vol 53 (19) ◽  
pp. 3393-3411 ◽  
Author(s):  
Jörg Frauhammer ◽  
Harald Klein ◽  
Gerhart Eigenberger ◽  
Ulrich Nowak
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Moving Grid ◽  
Boundary Problems

Fictitious domains and level sets for moving boundary problems. Applications to the numerical simulation of tumor growth

2011 ◽  
Vol 230 (4) ◽  
pp. 1335-1358 ◽  
Author(s):  
M. Carmen Calzada ◽  
Gema Camacho ◽  
Enrique Fernández-Cara ◽  
Mercedes Marín
Keyword(s):  
Numerical Simulation ◽  
Tumor Growth ◽  
Level Sets ◽  
Moving Boundary ◽  
Moving Boundary Problems ◽  
Boundary Problems
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