Reconstruction of Boundary Conditions of a Parabolic-Hyperbolic Transmission Problem

We consider a special kind of interface partial differential equations problems, which solution is defined in a few disjoint distant domains, where the effect of the intermediate region (layer) is modeled by means of nonlocal jump conditions across the layer. Our aim is the numerical identification of external boundary conditions for parabolic-hyperbolic problems on disjoint domains from given point data. We develop decomposition techniques to obtain exact formulas for the unknown boundary conditions. A number of numerical examples are discussed.