Geodesic
Weak solutions for a well-posed Hele-Shaw problem
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 397-424.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
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 $BV$, proviamo un teorema di comparazione, e mostriamo che la soluzione dipende in modo continuo dai dati iniziali e di contorno. 
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     title = {Weak solutions for a well-posed {Hele-Shaw} problem},
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Antontsev, S. N.; Meirmanov, A. M.; Yurinsky, V. V. Weak solutions for a well-posed Hele-Shaw problem. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 397-424. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a8/

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