Registered Data

[CT031]

  • Session Time & Room
    • CT031 (1/1) : 4C @G502 [Chair: Tomoharu Suda]
  • Classification
    • CT031 (1/1) : Topological dynamics (37B) / General higher-order partial differential equations and systems of higher-order partial differential equations (35G) / Smooth dynamical systems: general theory (37C)

[00502] The Helmholtz-Hodge decomposition of polynomial vector fields

  • Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
  • Type : Contributed Talk
  • Abstract : The Helmholtz-Hodge decomposition is a fundamental tool in the study of vector fields and has many applications. In this talk, we will focus on the case of polynomial vector fields. First, we will introduce results on the general properties and methods for finding a decomposition. As an application, we will explain the relationship between the Helmholtz-Hodge decomposition and the construction of Lyapunov functions.
  • Classification : 37B25, 31B99
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoharu Suda (RIKEN)
    • Tomoharu Suda (Keio University)

[00921] Inverse Coefficient Problem - Coupling Fourth and Second Order Equations

  • Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
  • Type : Contributed Talk
  • Abstract : In this paper, the recovery of the diffusion coefficient from the final time-measured data is carried out using the quasi-solution approach. The inverse coefficient problem is formulated as a minimization problem using an objective functional. The existence of the minimizer is proved, then the necessary optimality condition is derived, and by using that condition, the stability results are proved. To illustrate the efficiency of this method, numerical results are investigated using the conjugate gradient method.
  • Classification : 35G16, 35R30, 49K35, 49K20
  • Format : Talk at Waseda University
  • Author(s) :
    • NAVANEETHA KRISHNAN M (CENTRAL UNIVERSITY OF TAMIL NADU, THIRUVARUR - 610005)

[00532] Pullback Operator Methods in Dynamical Systems: Theory and Computation

  • Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
  • Type : Contributed Talk
  • Abstract : Koopman operator methods along with the associated numerical algorithms have provided a powerful methodology for the data-driven study of nonlinear dynamical systems. In this talk, we will give a brief outline of how the Koopman group of operators can be generalized beyond function spaces to the space of sections of various vector bundles over the state space. We describe their relationship with the standard Koopman operator on functions as well as describe the new spectral invariants produced by these generalized operators. We then demonstrate how the recently developed spectral exterior calculus framework can be utilized to compute the spectral properties of the generator of the induced operator on sections of the cotangent bundle. We conclude with some applications of the algorithm to some well-known dynamical systems.
  • Classification : 37C30
  • Format : Online Talk on Zoom
  • Author(s) :
    • Allan M. Avila (AIMdyn Inc.)