论文标题
边界域积分方程的一个新家族，用于与$ h^{ - 1}（ - ω）$ source on Lipschitz域中的不均匀介质中扩散方程的问题
A New Family of Boundary-Domain Integral Equations for the Dirichlet Problem of the Diffusion Equation in Inhomogeneous Media with $H^{-1}(Ω)$ Source Term on Lipschitz Domains
论文作者
论文摘要
非苯二烯介质中扩散方程的内部差异边界值问题将减少为使用（Fresneda-Portillo，2019）获得的边界域积分方程（BDIE）系统，与（Chkadua等人2009年）不同。 We further extend the results obtained in (Fresneda-Portillo, 2019) for the mixed problem in a smooth domain with $L^{2}(Ω)$ right hand side to Lipschitz domains and source term $f$ in the Sobolev space $H^{-1}(Ω)$, where neither the classical nor the canonical co-normal derivatives are well defined. BDIE系统与原始BVP之间的等效性与在适当的Sobolev空间中的解决性和解决方案唯一性一起证明了。
The interior Dirichlet boundary value problem for the diffusion equation in non-homogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in (Fresneda-Portillo, 2019) different from (Chkadua et. al 2009). We further extend the results obtained in (Fresneda-Portillo, 2019) for the mixed problem in a smooth domain with $L^{2}(Ω)$ right hand side to Lipschitz domains and source term $f$ in the Sobolev space $H^{-1}(Ω)$, where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces.
