Irregular morphologies in unstable hele-shaw free-boundary problems

A. A. Lacey; S. D. Howison; J. R. Ockendon; P. Wilmott

doi:10.1093/qjmam/43.3.387

Irregular morphologies in unstable hele-shaw free-boundary problems

A. A. Lacey, S. D. Howison, J. R. Ockendon, P. Wilmott

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Abstract

A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. This prediction involves an analytic continuation and the singularities encountered in the construction of the solution are related to those which are known to occur in exact solutions in the absence of surface tension. © 1990 Oxford University Press.

Original language	English
Pages (from-to)	387-405
Number of pages	19
Journal	Quarterly Journal of Mechanics and Applied Mathematics
Volume	43
Issue number	3
DOIs	https://doi.org/10.1093/qjmam/43.3.387
Publication status	Published - Aug 1990

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title = "Irregular morphologies in unstable hele-shaw free-boundary problems",

abstract = "A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. This prediction involves an analytic continuation and the singularities encountered in the construction of the solution are related to those which are known to occur in exact solutions in the absence of surface tension. {\textcopyright} 1990 Oxford University Press.",

author = "Lacey, {A. A.} and Howison, {S. D.} and Ockendon, {J. R.} and P. Wilmott",

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AU - Howison, S. D.

AU - Ockendon, J. R.

AU - Wilmott, P.

PY - 1990/8

Y1 - 1990/8

N2 - A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. This prediction involves an analytic continuation and the singularities encountered in the construction of the solution are related to those which are known to occur in exact solutions in the absence of surface tension. © 1990 Oxford University Press.

AB - A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. This prediction involves an analytic continuation and the singularities encountered in the construction of the solution are related to those which are known to occur in exact solutions in the absence of surface tension. © 1990 Oxford University Press.

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DO - 10.1093/qjmam/43.3.387

M3 - Article

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EP - 405

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

IS - 3

ER -

Irregular morphologies in unstable hele-shaw free-boundary problems

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