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Education
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1999.08
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Ph.D.
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Mathematics
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University of Wisconsin
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1990.02
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M.S.
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Mathematics
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Seoul National Univeristy
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1988.02
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B.S.
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Mathematics
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Seoul National Univeristy
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Academic
Positions
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2009.03~
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Associate Professor
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KAIST, Department of Mathematical Sciences
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2005.04~2009.02
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Assistant Professor
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KAIST, Department of Mathematical Sciences
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2004.09~2005.03
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Visiting Assistant Professor
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University of California at Riverside, Department of
Mathematics
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2003.08~2004.08
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Post-doctoral Associate
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University of Toronto, Fields Institute
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2002.09-2003.07
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Research Professor
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Kyunghee University, Impedance Image Research
Center
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2001.09~2002.08
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Visiting Assistant Professor
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University of Minnesota, Department of Mathematics
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1999.09~2001.08
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Post-doctoral Associate
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University of Minnesota, Institute of Mathematics
and its Application
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Research Interests
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Partial Differential Equations, Numerical Schemes for
Hyperbolic Equations, Fluid Dynamics, Asymptotics in Diffusive Problems,
Inverse Problem, Mathematical Modeling in Biological Development
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Research Papers: by topics, by years or from
Mathscinet
Lecture Notes
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4. fluid Mechanics (pdf file)
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3. Notating strategy for
systems of Partial differential equations (pdf file)
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2. Option Pricing
Modeling (pdf
file)
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1. Similarity &
Scaling Invariance in Convection and Diffusion (pdf file)
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Invited Presentations
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Date
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Event or Place
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Talk Title
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2008.07.08
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Asian Inverse Problem conference (Hanbat Univ.)
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Electrical impedance tomography on a resistive
network with internal current
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2009.05.11
-2009.05.13
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Korea & Australia Joint Analysis Forum
(POSTECH)
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A
generalization of moment problem to a complex density
and its application to the heat equation
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2009.04.01
-2009.04.04
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International Conference on Kinetic and Related
Models (Wuhan University, China)
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Long time convergence order in the Porous Medium
equation
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2009.02.02
-2009.02.03
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2009 NIMS Workshop on "Mathematical Analysis,
Numerics and Applications in fluid and gas dynamics"
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Fundamental solutions of a conservation laws
without convexity
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2009.01.29
-2009.01.31
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2009 NIMS Minicourse
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Structure of solutions to
conservation laws
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2008.07.08
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East China PDE Conference (Nanjing)
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Long time convergence order in the Porous Medium
equation
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2008.06.27
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Hanbat Univ. PDE Workshop
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Fundamental solutions of a conservation laws
without convexity
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2008.06.24
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KAIST-Fudan Univ. Joint workshop
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Fundamental solutions of a conservation laws
without convexity
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2008.05.19
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7th AIMS International Conference on Dyn.
Systems, Diff. Equations and Applications
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Potential comparison and asymptotics of equations
in a divergence form
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2008.02.27
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Univ. of Minnesota, School of Mathematics, PDE
seminar
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Fundamental solutions of a conservation laws
without convexity
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2008.01.28
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Postech math dept. PDE Conference
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2007.11.28
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KAIST dept. of Math Sci Colloquium
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Partial Differential Equations. Why & What.
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2007.11.14
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Sungkyunkwan Univ. PDE seminar
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Fundamental solutions of conservation laws
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2007.10.12
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Postech math dept. Colloquium
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¿Ö Æí¹ÌºÐ¹æÁ¤½ÄÀ» ÇÏ°Ô µÇ°í ¶Ç ¹«¾ùÀ» ÇÏ°íÀÚ Çϴ°¡.
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2007.06.28
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2007 JNU Math Workshop on Numerical Analysis
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Computation
of a thin film equation: high order
diffusion
versus convection
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2007.06.11
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NIMS International Workshop on
Fluid Dynamics
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Computation
of a thin film equation: high order
diffusion
versus convection
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2007.06.08
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SNU Workshop on Nonlinear Partial Differential
Equations
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The optimal
convergence order of radial solutions to p-Laplacian and PME
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2007.06.02
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Second Workshop on Nonlinear Partial Differential
Equations (International Workshop among Asian Countries)
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Evolution of Radial Solutions
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PDE LAB Funded Research Projects
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Period
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Project Title
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Sponsor
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Participants
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2009.05-2012.02
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Virtual resistive network & a development of an
anisotropic conductivity reconstruction method for a medical imaging
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KOSEF (KW290,000,000)
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Á¤Àçȯ,À̹αâ,
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2008.07-2009.06
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The role of morphogen in biological development and its mathematical
analysis and modeling
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KAIST (HRHRP) (KW 30,000,000)
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Á¶ÀºÁÖ
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2007.05-2009.02
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Evolution of radial solutions in
compressible fluid dynamics: asymptotics and regularity at the origin
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KOSEF
(KW151,000,000)
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±è¹ÌÁ¤, ÀÌ¿µ¶õ, Á¤½ÂÈÆ
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2006.09-2007.08
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¼±Ã¼±¸Á¶ÀÇ Á±¼ ¹× ÃÖÁ¾°µµ¿¡ ´ëÇÑ Çؼ®Àû ±â¹ý °³¹ß
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Korea ship evaluation Inc.
(KW 25,000,000)
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ÀÌâ¿Á, Á¤Àçȯ, ±è»ó¾ð
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2006.07-2007.06
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Development of potential comparison technique
and convergence study in several nonlinear dynamics
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KRF
(KW 38,170,000)
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Á¤Àçȯ
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Research Projects & Interests
(2008-06-15)
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A.
Long
time asymptotics in nonlinear diffusion and convection.
The long time
contraction order of a nonlinear diffusion equations have been studied for
last two decades for various cases. Some of them are optimal ones and
however many of them are not. Recently we have developed a potential
comparison principle and obtained optimal convergence orders for certain
cases in fast diffusion equations. This technique seems applicable to a
large class of problems including nonlinear diffusion and convection. The
optimal convergence order is also related to the moments of the problem.
For example, if two solutions share the same moments up to certain order
than it seems guarantee better contraction order. In the analysis the
monotonicity of the intersection points is useful. Hence the Sturmian type
theory should be developed for nonlinear diffusion equations. Another
building block is the steepness of source-type solutions. For example the
Aronson-Banilan type estimate gives that the Barenblatt type solution is
the steepest one. For more general cases it seems true and we are working
on this kind of problems.
B.
Mathematical
modeling for the biological development.
It is clear that
the biology is the source of the mathematical problems of the next
generation and it will play the role that mechanics or dynamics did to
mathematics. We are interested in the development of the imaginary wing
disk of Drosophila. In particular we are interested in the role of
morphogen in the pattern formation. The goal of this project is to analyze
the phenomena quantitatively and to model the pattern formation together
with the growth.
C.
Inverse
Problem for the Conductivity Recovery.
The conductivity
of a body shows how the electrical current flows in the body when a voltage
difference or current injection is given on the boundary of the body. In
particular, if one can find the conductivity map of a human body it has
great importance. For example, in the cardiopulmonary
resuscitation technique, doctors perform it based on experience. However,
if we know a conductivity map that one can greatly reduce the risk of side
effects such as burned internal organs. We are interested in obtaining a
good static image. However, the current technique is far from obtaining it.
We are developing a MREIT model using current laws rather than voltage
laws. In this project we are interest in the stability analysis and obtain
more stable and fast algorithm that may gives three dimensional
conductivity.
D.
Numerical
Schemes for Convection.
We have been
worked on the study of numerical schemes for the convection equations.
Godunov, WENO, central, upwind, positive, Lax-Wendroff schemes are
examples. These schemes are for convection equations and are widely used to
solve various kinds of problems. We found that, even if those schemes are
used by lots of people, there are many hidden properties. It is also interesting
topic to work with higher order diffusion terms that frequently appears in
thin film equations. We are interested in survey the properties of
numerical schemes and develop better schemes for various situations.
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