Displaying similar documents to “On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.”

On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary

Olga A. Oleinik, Tatiana A. Shaposhnikova (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].

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...

Remarks on the equatorial shallow water system

Chloé Mullaert (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.