DOI: 10.1155/aaa/9099201 ISSN: 1085-3375
Analysis of Boundary‐Domain Integro‐Differential Equations Based on the Stationary Parametrix for Nonstationary Diffusion Variable Coefficient Dirichlet Initial Boundary Value Problem
Bira Wolteji Ujulu, Tamirat Temesgen DuferaThis paper investigates the direct segregated boundary‐domain integrodifferential equations (BDIDEs) associated with the Dirichlet initial boundary value problem (IBVP) for nonstationary diffusion partial differential equations (PDEs) with variable coefficient, in appropriate Sobolev‐type Banach‐valued spaces. By employing a stationary parametrix (Levi function), we transformed the IBVP into an equivalent system of BDIDEs. Subsequently, the properties of the parametrix‐based potential operators are analyzed in Sobolev‐type Banach‐valued spaces, and the equivalence between the original problem and the transformed system is rigorously established.