论文标题
在形状和拓扑优化问题上与Helmholtz方程和光谱问题的约束
On shape and topological optimization problems with constraints Helmholtz equation and spectral problems
论文作者
论文摘要
沿海侵蚀描述了由潮汐，波浪或电流引起的运动引起的沙子的位移。其某些波浪现象是由Helmholtz型方程建模的。在本文中，我们的目的首先是研究最佳形状障碍，以在Helmholtz方程的约束下减轻沙子传输。这项工作的第二侧与Dirichlet和Neumann Spectral问题有关。我们在一套可允许的准公开集中显示了最佳形状的存在。并在常规框架中给出必要的一阶最佳条件。
Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modeled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal shapes obstacles to mitigate sand transport under the constraint of the Helmholtz equation. And the second side of this work is related to Dirichlet and Neumann spectral problems.We show the existence of optimal shapes in a general admissible set of quasi open sets. And necessary optimality conditions of first order are given in a regular framework.
