Extra Form
강연자 이형천
소속 아주대
date 2016-06-09

Many mathematical and computational analyses have been performed for deterministic partial differential equations (PDEs) that have perfectly known input data. However, in reality, many physical and engineering problems involve some level of uncertainty in their input, e.g., unknown properties of the material, the lack of information on boundary data, etc. One effective and realistic means for modeling such uncertainty is through stochastic partial differential equations (SPDEs) using randomness for uncertainty. In fact, SPDEs are known to be effective tools for modeling complex physical and engineering phenomena. In this talk, we propose and analyze some optimal control problems for partial differential equations with random coefficients and forcing terms.
These input data are assumed to be dependent on a finite number of random variables. We set up three different kind of problems and prove existence of optimal solution and derive an optimality system. In the method, we use a Galerkin approximation in physical space and a sparse grid collocation in the probability space. We provide a comparison of these three cases for fully discrete solution using an appropriate norm and analyze the computational efficiency.

첨부 '1'
  1. An introduction to hyperplane arrangements

  2. 14Jun
    by 김수현
    in 수학강연회

    Analysis and computations of stochastic optimal control problems for stochastic PDEs

  3. Analytic torsion and mirror symmetry

  4. Anomalous diffusions and fractional order differential equations

  5. Arithmetic of elliptic curves

  6. Averaging formula for Nielsen numbers

  7. Birational Geometry of varieties with effective anti-canonical divisors

  8. Brownian motion and energy minimizing measure in negative curvature

  9. Brownian motion with darning and conformal mappings

  10. Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras

  11. Categorification of Donaldson-Thomas invariants

  12. Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds

  13. Circular maximal functions on the Heisenberg group

  14. Class field theory for 3-dimensional foliated dynamical systems

  15. Classical and Quantum Probability Theory

  16. Cloaking via Change of Variables

  17. Codimension Three Conjecture

  18. Combinatorial Laplacians on Acyclic Complexes

  19. Compressible viscous Navier-Stokes flows: Corner singularity, regularity

  20. Conformal field theory and noncommutative geometry

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 Next
/ 12