Global in time solution to the Hele-Shaw problem with a change of topology

Anvarbek M. Meirmanov; Boris Zaltzman

doi:10.1017/S0956792502004874

Global in time solution to the Hele-Shaw problem with a change of topology

Anvarbek M. Meirmanov
, Boris Zaltzman

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The existence of classical solutions with a free boundary changing its topology in time is proved for the multi-dimensional Hele-Shaw problem. We prove that, if some symmetry and monotonicity conditions on the problem data hold, then a cusp, arising at the contact between two free boundary components, disappears instantly and the free boundary becomes smooth and singly-connected.

Original language	English
Pages (from-to)	431-447
Number of pages	17
Journal	European Journal of Applied Mathematics
Volume	13
Issue number	4
DOIs	https://doi.org/10.1017/S0956792502004874
State	Published - 1 Aug 2002

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1017/S0956792502004874

Cite this

@article{adcc4b56d31a42b1a3e2597fbc99243e,

title = "Global in time solution to the Hele-Shaw problem with a change of topology",

abstract = "The existence of classical solutions with a free boundary changing its topology in time is proved for the multi-dimensional Hele-Shaw problem. We prove that, if some symmetry and monotonicity conditions on the problem data hold, then a cusp, arising at the contact between two free boundary components, disappears instantly and the free boundary becomes smooth and singly-connected.",

author = "Meirmanov, \{Anvarbek M.\} and Boris Zaltzman",

year = "2002",

month = aug,

day = "1",

doi = "10.1017/S0956792502004874",

language = "English",

volume = "13",

pages = "431--447",

journal = "European Journal of Applied Mathematics",

issn = "0956-7925",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - Global in time solution to the Hele-Shaw problem with a change of topology

AU - Meirmanov, Anvarbek M.

AU - Zaltzman, Boris

PY - 2002/8/1

Y1 - 2002/8/1

N2 - The existence of classical solutions with a free boundary changing its topology in time is proved for the multi-dimensional Hele-Shaw problem. We prove that, if some symmetry and monotonicity conditions on the problem data hold, then a cusp, arising at the contact between two free boundary components, disappears instantly and the free boundary becomes smooth and singly-connected.

AB - The existence of classical solutions with a free boundary changing its topology in time is proved for the multi-dimensional Hele-Shaw problem. We prove that, if some symmetry and monotonicity conditions on the problem data hold, then a cusp, arising at the contact between two free boundary components, disappears instantly and the free boundary becomes smooth and singly-connected.

UR - https://www.scopus.com/pages/publications/0036671602

U2 - 10.1017/S0956792502004874

DO - 10.1017/S0956792502004874

M3 - Article

AN - SCOPUS:0036671602

SN - 0956-7925

VL - 13

SP - 431

EP - 447

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

IS - 4

ER -

Global in time solution to the Hele-Shaw problem with a change of topology

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this