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Lebedev Pavel Dmitrievich

Publications in Math-Net.Ru

  1. Newton's method in constructing a singular set of a minimax solution in a class of boundary value problems for the Hamilton — Jacobi equations

    Chelyab. Fiz.-Mat. Zh., 9:1 (2024),  63–76
  2. On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems

    Izv. IMI UdGU, 63 (2024),  37–48
  3. Numerical-analytical construction of a generalized solution of the eikonal equation in the plane case

    Mat. Sb., 215:9 (2024),  99–124
  4. On the problem of covering spherical figures with equal spherical caps

    Trudy Inst. Mat. i Mekh. UrO RAN, 30:1 (2024),  142–155
  5. Alpha sets and their hulls: analytical relationships in the plane case

    Russian Universities Reports. Mathematics, 29:146 (2024),  204–217
  6. Algorithms for constructing optimal covering of planar figures with disks sets of linearly different radii

    Bulletin of Irkutsk State University. Series Mathematics, 46 (2023),  35–50
  7. Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices

    Izv. IMI UdGU, 61 (2023),  76–93
  8. Algorithms of optimal covering of 2D sets with dynamical metrics

    Izv. IMI UdGU, 60 (2022),  58–72
  9. Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface

    Ural Math. J., 8:2 (2022),  115–126
  10. Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons

    Izv. IMI UdGU, 57 (2021),  142–155
  11. On the analytical construction of solutions for one class of time-optimal control problems with nonconvex target set

    Trudy Inst. Mat. i Mekh. UrO RAN, 27:3 (2021),  128–140
  12. Iterative algorithms for constructing the thinnest coverings of convex polyhedra by sets of different balls

    Trudy Inst. Mat. i Mekh. UrO RAN, 27:1 (2021),  116–129
  13. On singularity structure of minimax solution to Dirichlet problem for eikonal type equation with discontinuous curvature of boundary of boundary set

    Ufimsk. Mat. Zh., 13:3 (2021),  129–154
  14. On the structure of the singular set of solutions in one class of 3D time-optimal control problems

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021),  471–486
  15. Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons

    Chelyab. Fiz.-Mat. Zh., 5:2 (2020),  218–232
  16. Numerical methods for constructing suboptimal packings of nonconvex domains with curved boundary

    Diskretn. Anal. Issled. Oper., 27:4 (2020),  58–79
  17. On covering bounded sets by collections of circles of various radii

    Bulletin of Irkutsk State University. Series Mathematics, 31 (2020),  18–33
  18. Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature

    Izv. IMI UdGU, 55 (2020),  93–112
  19. Properties of non stationer pseudo vertex with the break of smoothness of the target set boarder curvature in the Dirichlet problem to eikonal type equation

    Sib. Èlektron. Mat. Izv., 17 (2020),  2028–2044
  20. Numerical methods for the construction of packings of different balls into convex compact sets

    Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020),  173–187
  21. Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set

    Russian Universities Reports. Mathematics, 25:132 (2020),  370–386
  22. Algorithms for solving the velocity problem with circular vectogram in inhomogeneous medium

    Chelyab. Fiz.-Mat. Zh., 4:4 (2019),  387–397
  23. Iterative methods for approximations constructing of optimal covering for nonconvex plane sets

    Chelyab. Fiz.-Mat. Zh., 4:1 (2019),  5–17
  24. Construction of a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary

    Izv. IMI UdGU, 53 (2019),  98–114
  25. Construction of optimal covers by disks of different radii for convex planar sets

    Trudy Inst. Mat. i Mekh. UrO RAN, 25:2 (2019),  137–148
  26. Construction of a nonsmooth solution in a time-optimal problem with a low order of smoothness of the boundary of the target set

    Trudy Inst. Mat. i Mekh. UrO RAN, 25:1 (2019),  108–119
  27. Algorithms of optimal ball packing into ellipsoids

    Izv. IMI UdGU, 52 (2018),  59–74
  28. Iterative methods for the construction of planar packings of circles of different size

    Trudy Inst. Mat. i Mekh. UrO RAN, 24:2 (2018),  141–151
  29. Euclidean distance to a closed set as a minimax solution of the Dirichlet problem for the Hamilton-Jacobi equation

    Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018),  797–804
  30. Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018),  59–73
  31. Algorithms for constructing optimal $n$-networks in metric spaces

    Avtomat. i Telemekh., 2017, no. 7,  141–155
  32. Iterative methods for minimization of the Hausdorff distance between movable polygons

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017),  86–97
  33. Algorithms of optimal packing construction in ellipse

    Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:3 (2017),  67–79
  34. Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

    Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017),  768–782
  35. Some facts about the Ramsey model

    Trudy Inst. Mat. i Mekh. UrO RAN, 22:3 (2016),  160–168
  36. Construction of the optimal result function and dispersing lines in time-optimal problems with a nonconvex target set

    Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  188–198
  37. The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set

    Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  282–293
  38. Algorithms of optimal set covering on the planar $\mathbb{R}^2 $

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:2 (2016),  258–270
  39. Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space

    Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  276–288
  40. Algorithms of optimal packing construction for planar compact sets

    Num. Meth. Prog., 16:2 (2015),  307–317
  41. Optimization of the Hausdorff distance between sets in Euclidean space

    Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  291–308
  42. Approximation of polygons with the best set of circles

    Bulletin of Irkutsk State University. Series Mathematics, 6:3 (2013),  72–87
  43. Approximation of nonsmooth optimal result in one class of velocity problems

    Vestnik Chelyabinsk. Gos. Univ., 2013, no. 16,  71–77
  44. Geometry of singular curves for one class of velocity

    Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 3,  157–167
  45. Algorithms of the best approximations of the flat sets by the union of circles

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  88–99
  46. A variant of a metric for unbounded convex sets

    Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013),  40–49
  47. Approximating sets on a plane with optimal sets of circles

    Avtomat. i Telemekh., 2012, no. 3,  79–90
  48. On approximate construction of controlled system reachable sets on finite time interval

    Izv. IMI UdGU, 2012, no. 1(39),  94
  49. Differential games with fixed terminal time and estimation of the instability degree of sets in these games

    Trudy Mat. Inst. Steklova, 277 (2012),  275–287
  50. On the set of limit values of local diffeomorphisms in wavefront evolution

    Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  171–185
  51. Defect of stability in game-pursuit problem

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  87–103
  52. Singularities' of Optimal-Time Function in One Class of Optimal-Time Control Problems Construction Algorithms

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  30–41
  53. Construction of the optimal outcome function for a time-optimal problem on the basis of a symmetry set

    Avtomat. i Telemekh., 2009, no. 7,  50–57
  54. On the coincidence of maximal stable bridges in two approach game problems for stationary control systems

    Trudy Inst. Mat. i Mekh. UrO RAN, 15:3 (2009),  219–240
  55. Procedures for calculating the nonconvexity measures of a plane set

    Zh. Vychisl. Mat. Mat. Fiz., 49:3 (2009),  431–440
  56. Geometry and the asymptotics of wave forms

    Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 3,  27–37
  57. Условия трансверсальности ветвей решения нелинейного уравнения в задаче быстродействия с круговой индикатрисой

    Trudy Inst. Mat. i Mekh. UrO RAN, 14:4 (2008),  82–99
  58. Construction of a minimax solution for an eikonal-type equation

    Trudy Inst. Mat. i Mekh. UrO RAN, 14:2 (2008),  182–191
  59. Construction of the function of the best result for the system with simple dynamic

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  152–154
  60. Вычисление меры невыпуклости плоских множеств

    Trudy Inst. Mat. i Mekh. UrO RAN, 13:3 (2007),  84–94
  61. On the geometry of wave fronts

    Izv. IMI UdGU, 2006, no. 3(37),  79–80

© Steklov Math. Inst. of RAS, 2024