Displaying similar documents to “The asymptotic behavior at the large time of solutions of some mathematical physics problems”

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 B ⁢ V spaces, prove a comparison theorem, and show that the solution depends continuously on...