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We consider a coupled $1D$ heat-wave system which serves as a simplifiedfluid-structure interaction problem. The system is coupled in two differentways: the first, when the interface does not have mass and the second, when theinterface does have mass. We prove an optimal regularity result in Sobolevspaces for both cases. The main idea behind the proof is to reduce the coupledproblem to a single nonlocal equation on the interface by using Neummann toDiriclet operator. Furthermore, we show that point mass coupling regularizesthe problem and quantify this regularization in the sense of Sobolev spaces.

A note on optimal regularity and regularizing effects of point mass coupling for a heat-wave system