  We consider a generalization of the inverse problem of the
electrocardiography in the framework of the theory of elliptic and parabolic
differential operators. More precisely, starting with the standard bidomain
mathematical model related to the problem of the reconstruction of the
transmembrane potential in the myocardium from known body surface potentials we
formulate a more general transmission problem for elliptic and parabolic
equations in the Sobolev type spaces and describe conditions, providing
uniqueness theorems for its solutions. Next, the new transmission problem is
interpreted in the framework of the elasticity theory applied to composite
media. Finally, we prove a uniqueness theorem for an evolutionary transmission
problem that can be easily adopted to many models involving the diffusion type
equations.
