Weak solutions for a well-posed Hele-Shaw problem
S. N. Antontsev, A. M. Meirmanov, V. V. Yurinsky (2004)
Bollettino dell'Unione Matematica Italiana
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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 spaces, prove a comparison theorem, and show that the solution depends continuously on...