论文标题
关于在2D无界域上定义的非均匀传热方程的dirichlet问题边界域积分方程的解决方案的存在和唯一性
On the Existence and Uniqueness of Solution of Boundary-Domain Integral Equations for the Dirichlet Problem for the Non-Homogeneous Heat Transfer Equation defined on a 2D Unbounded Domain
论文作者
论文摘要
从二维介质中定义的非均匀介质中的扩散方程的dirichlet问题获得了分离的边界域积分方程（BDIE）的系统。我们使用的参数与In（Dufera，2019年）使用的参数不同。 BDIS系统是根据基于参数的表面和体积电势制定的，其映射属性在加权的Sobolev空间中进行了分析。证明BDIE的系统等效于原始边界值问题，并且可以在适合无限域的适当加权Sobolev空间中唯一解决。
A system of segregated boundary-domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in non-homogeneous media defined on an exterior two-dimensional domain. We use a parametrix different from the one employed by in (Dufera, 2019). The system of BDIEs is formulated in terms of parametrix-based surface and volume potentials whose mapping properties are analysed in weighted Sobolev spaces. The system of BDIEs is shown to be equivalent to the original boundary value problem and uniquely solvable in appropriate weighted Sobolev spaces suitable for infinite domains.
