Toufic El Arwadi, Toni Sayah
Abstract:
In this article, we consider the time dependent linear
elliptic problem with dynamic boundary condition. We recall the
corresponding Dirichlet-to-Neumann operator on
denoted by
.
Then we show that when
near the
boundary,
is bounded by
in
norm. This result is a generalization of the bound
with the
norm and is applicable for comparing the
Dirichlet to Neumann semigroup and the Lax semigroup. Finally, we
present numerical experiments for validation of our results.
Submitted September 5, 2015. Published October 2, 2015.
Math Subject Classifications: 47D06, 47A99, 35J15, 35M13, 65M60.
Key Words: Dynamic boundary condition; Dirichlet-to-Neumann operator;
Lp estimation; finite element method.
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Toufic El Arwadi Department of Mathematics and computer science Faculty of Science, Beirut Arab university P.O. Box: 11-5020, Beirut, Lebanon email: t.elarwadi@bau.edu.lb | |
Toni Sayah Research unit "EGFEM", Faculty of sciences Saint-Joseph University B.P. 11-514 Riad El Solh Beirut 1107 2050, Lebanon email: toni.sayah@usj.edu.lb |
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