论文标题
基于无界域上新的参数家族的不均匀介质中扩散方程的混合问题的边界域积分方程
Boundary-Domain Integral Equations for the Mixed Problem for the Diffusion Equation in Inhomogeneous Media based on a New Family of Parametrices on Unbounded Domains
论文作者
论文摘要
边界域积分方程的系统源自在无界域上定义的不均匀介质中扩散方程的混合（Dirichlet-Neumann）边界值问题。边界域积分方程是根据基于参数的电位类型积分运算符来制定的，在边界和域上定义。分析了基于参数的势能在加权Sobolev空间上的映射属性。显示了原始边界值问题与BDIE系统之间的等效性。使用Fredholm的替代方案和紧凑性参数证明了BDIE解决方案的唯一性。
A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are formulated in terms of parametrix-based potential type integral operators defined on the boundary and the domain. Mapping properties of parametrix-based potentials on weighted Sobolev spaces are analysed. Equivalence between the original boundary value problem and the system of BDIEs is shown. Uniqueness of solution of the BDIEs is proved using Fredholm Alternative and compactness arguments adapted to weigthed Sobolev spaces.
