Weak solutions for a well-posed Hele-Shaw problem
Antontsev, S. N. ; Meirmanov, A. M. ; Yurinsky, V. V.
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 397-424 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Analizziamo l'esistenza e l'unicità di soluzioni deboli del problema ben posto di Hele-Shaw con condizioni generali sul contorno assegnato, equazione governante non-omogenea nel dominio incognito e condizione dinamica non-omogenea a contorno libero. Il nostro approccio permette anche di indebolire le restrizioni sui dati iniziali e di contorno. Otteniamo infine alcune stime per la soluzione negli spazi B⁢V, proviamo un teorema di comparazione, e mostriamo che la soluzione dipende in modo continuo dai dati iniziali e di contorno.

Publié le : 2004-06-01
@article{BUMI_2004_8_7B_2_397_0,
     author = {S. N. Antontsev and A. M. Meirmanov and V. V. Yurinsky},
     title = {Weak solutions for a well-posed Hele-Shaw problem},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {397-424},
     zbl = {1177.76398},
     mrnumber = {2072944},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_397_0}
}

Antontsev, S. N.; Meirmanov, A. M.; Yurinsky, V. V. Weak solutions for a well-posed Hele-Shaw problem. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 397-424. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_397_0/

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