arXiv subjects
Publications and source records attributed to Sergey B. Tikhomirov.
An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stability of solution is studied in various functional classes.
We call that a vector field has the oriented shadowing property if for any $\varepsilon>0$ there is $d>0$ such that each $d$-pseudo orbit is $\varepsilon$-oriented shadowed by some real orbit. In this paper, we show that the $C^1$-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $Ω$-stability.