On a Bernoulli problem with geometric constraints
On a Bernoulli problem with geometric constraints
复制标题
具有几何约束的伯努利问题
DOI：
10.1051/cocv/2010049
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Y. Privat
中科院分区：
文献类型：
--
作者：
A. Laurain;Y. Privat
研究了带几何约束的Bernoulli自由边界问题。定义域Ω被约束为位于由x1 ≥ 0确定的半空间中，其边界包含超平面{x1 =0 }的一段，其中施加非齐次Dirichlet条件。然后，我们正在寻找的解决方案的偏微分方程同时满足狄利克雷和诺依曼边界条件的自由边界。解的存在性和唯一性已经得到了解决，本文首先致力于研究解的几何和渐进性质，然后使用形状优化公式对问题进行数值处理。本文的主要难点和创新之处在于几何约束的处理。
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 =0 } where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.