论文标题
三维内部包含的热方程式产生的有效边界条件
Effective Boundary Conditions Arising from the Heat Equation with Three-dimensional Interior Inclusion
论文作者
论文摘要
我们研究包含薄层的域中的热方程的初始边界值问题。层的导热率与大部分域的导热率截然不同。此外，该层是各向异性的，``最佳对齐''的意义是，该层的正常方向始终是热张量的特征向量。为了揭示层的效果，我们将其视为“有效边界条件”（EBC）在最初的边界值的限制中满足``有效的边界条件''的无用表面。这些EBC富含多样性和类型，包括一些非标准的EBC，例如Dirichlet到Neumann映射和分数Laplacian。
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and ``optimally aligned" in the sense that the normal direction in the layer is always an eigenvector of the thermal tensor. To reveal the effects of the layer, we regard it as a thickless surface on which ``effective boundary conditions" (EBCs) are satisfied by the limit of solutions of the initial boundary value problem as the thickness of the layer shrinks to zero. These EBCs are rich in variety and type, including some nonstandard ones such as the Dirichlet-to-Neumann mapping and the fractional Laplacian.
