Affiliation:
1. Institute of Mathematics and Computer Science , Siberian Federal University , pr. Svobodnyi 79, 660041 Krasnoyarsk , Russia
Abstract
Abstract
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.
Funder
Foundation for the Advancement of Theoretical Physics and Mathematics