Weak solutions for a well-posed Hele-Shaw problem

S. N. Antontsev; A. M. Meirmanov; V. V. Yurinsky

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 2, page 397-424
  • ISSN: 0392-4041

Abstract

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We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in B ⁢ V spaces, prove a comparison theorem, and show that the solution depends continuously on the initial and boundary data.

How to cite

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Antontsev, S. N., Meirmanov, A. M., and Yurinsky, V. V.. "Weak solutions for a well-posed Hele-Shaw problem." Bollettino dell'Unione Matematica Italiana 7-B.2 (2004): 397-424. <http://eudml.org/doc/194598>.

@article{Antontsev2004,
abstract = {We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in $BV$ spaces, prove a comparison theorem, and show that the solution depends continuously on the initial and boundary data.},
author = {Antontsev, S. N., Meirmanov, A. M., Yurinsky, V. V.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {397-424},
publisher = {Unione Matematica Italiana},
title = {Weak solutions for a well-posed Hele-Shaw problem},
url = {http://eudml.org/doc/194598},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Antontsev, S. N.
AU - Meirmanov, A. M.
AU - Yurinsky, V. V.
TI - Weak solutions for a well-posed Hele-Shaw problem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/6//
PB - Unione Matematica Italiana
VL - 7-B
IS - 2
SP - 397
EP - 424
AB - We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in $BV$ spaces, prove a comparison theorem, and show that the solution depends continuously on the initial and boundary data.
LA - eng
UR - http://eudml.org/doc/194598
ER -

References

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