The inverse problem of determining a source in the stationary transport equation for a Hamiltonian system
The article is devoted to the problem, mentioned in its title, on manifolds. The main aim is to extend the author's previous existence results for Hamiltonians, quadratic in momentum variable, to Hamiltonians, which are convex and positively homogeneous in momentum. The consideration is based on some new deep constructions in the geometry of cotangent bundles. In particular, the author introduces the so-called bundle of semibasic tensors over a cotangent bundle and the so-called horizontal covariant derivative, playing a central role in the proof of results.
scientific article; zbMATH DE number 1023992