Speciality:
01.01.07 (Computing mathematics)
Birth date:
28.11.1969
E-mail: ;
Keywords: numerical analysis,
globally stable approximation schemes,
approximation attractor of a semidynamical system,
numerical methods for a plasmas dynamics.
Subject:
1991–1996: numerical methods and differential theorems for the new mathematical models for Steady Self-focusing of Electromagnetic Beams in Plasma. 1996–present: an approach to verify continuity of a global attractor of a semidynamical system with a parameter is presented. This approach makes it possible to establish a connection between upper and lower semicontinuity of a global attractor and boundedness as a function of rate of attraction to a attractor. An approach to approximate a global attractor of a semidynamical system with error estimates in Hausdorff metric is studied. This approach is based on the properties of a function of rate of attraction to an attractor and on some new results for an unstable manifold in a neighborhood of an essential nonhyperbolical point.
Main publications:
Kornev A. A. On the peculiarity of the focus type in the solutions of a self-focusing problem with allowance for relativistic and striction nonlinearities // Russian J. Numer. Anal. Math. Modelling, 1997, 12(5), 436–442.
