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Extra Form
Lecturer 이형천
Dept. 아주대
date Jun 09, 2016

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.


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List of Articles
Category Subject Dept. Lecturer
Math Colloquia Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
Math Colloquia Compressible viscous Navier-Stokes flows: Corner singularity, regularity file POSTECH 권재룡
Math Colloquia Combinatorial Laplacians on Acyclic Complexes file 서울대학교 국웅
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia Cloaking via Change of Variables file KAIST 임미경
Math Colloquia Classical and Quantum Probability Theory file 충북대학교 지운식
Math Colloquia Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
Math Colloquia Circular maximal functions on the Heisenberg group file 연세대 수학과 김준일
Math Colloquia Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds file KIAS 박진성
Math Colloquia Categorification of Donaldson-Thomas invariants file 서울대학교 김영훈
Math Colloquia Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
Math Colloquia Brownian motion with darning and conformal mappings file University of Washington Zhen-Qing Chen
Math Colloquia Brownian motion and energy minimizing measure in negative curvature file 서울대학교 임선희
Math Colloquia Birational Geometry of varieties with effective anti-canonical divisors file 연세대학교 최성락
Math Colloquia Averaging formula for Nielsen numbers file 서강대학교 이종범
Math Colloquia Arithmetic of elliptic curves file 서울대 김도형
Math Colloquia Anomalous diffusions and fractional order differential equations file University of Washington Zhen-Qing Chen
Math Colloquia Analytic torsion and mirror symmetry file Kyoto University Ken-ichi Yoshikawa
Math Colloquia Analysis and computations of stochastic optimal control problems for stochastic PDEs file 아주대 이형천
Math Colloquia An introduction to hyperplane arrangements file 서울대 이승진
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