Time local existence of a moving boundary of the Hele-Shaw flow with suction

European Journal of Applied Mathematics

Volumn 10, Issue 6, 1999, Pages 581-605

  Kimura, M ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033264730     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792599003897     Document Type: Article

References (17)

1. CHEN, X., HONG, J. & YI, F. (1996) Existence, uniqueness, and regularity of classical solutions of the Mullins-Sekerka problem. Comm. Partial Diff. Eq. 21, 1705-1727.
2. DAVIS, P. J. (1974) The Schwarz function and its applications. Carus Math. Monographs, 17. Mathematical Association of America.
3. DUCHON, J. & ROBERT, R. (1984) Évolution d'une interface par capillarité et diffusion de volume I. Existence locale en temps. Ann. Inst. Henri Poincaré. Analyse non linéaire, 1, 361-378.
4. ESCHER, J. & SIMONETT, G. (1997) Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations, 2, 619-642.
5. GUSTAFSSON, B. (1985) Applications of variational inequalities to a moving boundary problem for Hele Shaw flows. SIAM J. Math. Anal 16, 279-300.
6. HELE-SHAW, H. S. (1898) The flow of water. Nature, 58, 34-36.
7. HENRICI, P. (1986) Applied and computational complex analysis: vol.3. Pure and Applied Mathematics, Wiley-Interscience. John Wiley & Sons, New York.
8. HOWISON, S. D. (1986) Fingering in Hele-Shaw cells. J. Fluid Mech. 167, 439-453.
9. HOWISON, S. D. (1992) Complex variable methods in Hele-Shaw moving boundary problems. Euro. J. Appl. Math. 3, 209-224.
10. HOWISON, S. D., OCKENDON, J. R. & LACEY, A. A. (1985) Singularity development in moving-boundary problems. Quart. J. Mech. Appl. Math. 38, 343-360.
11. KINDERLEHRER, D. & STAMPACCHIA, G. (1980) An Introduction to Variational Inequalities and their Applications. Academic Press.
12. LAMB, H. (1932) Hydrodynamics. 6th ed. Cambridge University Press.
13. PETERSON, L. (1981) Radial fingering in a Hele-Shaw cell. J. Fluid Mech. 113, 513-529.
14. PETROVSKY, I. (1954) Lectures on Partial Differential Equations. Interscience Publishers.
15. RICHARDSON, S. (1972) Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel. J. Fluid Mech. 56, 609-618.
16. TABELING, P., ZOCCHI, G. & LIBCHABER, A. (1987) An experimental study of the Saffman Taylor instability. J. Fluid Mech. 177, 67-82.
17. TREVES, F. (1975) Basic linear partial differential equations, Academic Press.