Schedule of the conference with abstracts

2009/11/05, Thursday morning session

Time: 9:10-10:00

Speaker: Eiji Yanagida

Affiliation: Tohoku University, JAPAN

Email: yanagida.AT.math.tohoku.ac.jp

Title: Connecting orbits for a semilinear parabolic equation with a supercritical exponent

Abstract:

Time: 10:10-10:50

Speaker: Sun-Sig Byun

Affiliation: Seoul National University

Email: byun.AT.snu.ac.kr

Title: Gradient Estimates for Elliptic and Parabolic PDEs with Measurable Coefficients in Nonsmooth Domains

Abstract: We find a minimal regularity requirement on the coefficients and a lowest level of geometric condition on the boundary for a classical Calderon-Zygmund estimate. 

Time: 11:00-11:40

Speaker: Minkyu Kwak

Affiliation: Chonnam National University

Email: mkkwak.AT.jnu.ac.kr

Title: The cone property for parabolic partial differential equations

Abstract: We show that a class of parabolic partial differential equations satisfy a cone property. This result implies that the projection from the global attractor to a finite dimensional Fourier space is injective and thus the global attractor becomes a finite dimensional graph.

Time: 11:50-12:30

Speaker: Ki-Ahm Lee

Affiliation: Seoul National University

Email: kiahm.AT.math.snu.ac.kr

Title: Parabolic Method for Nonlinear Eigen Value Problems

Abstract: In this talk, we are going to discuss the parabolic approach on the nonlinear eigen-value problems and its recent development. The geometric structure of the nonnegative first eigen function of Linear or Nonlinear eigen value problems has been studied to understand the ground state in Physics, asymptotic behavior of the parabolic flows, and its own interest in elliptic PDE. There has been H.J. Brascamp and E.H. Lieb's method based on probability, and N.J. Korevaar's method which can be applicable to linear or sub-linear case. Parabolic approach has been developed to deal with super-linear case. Such idea has been extended to eigen-value problems for nonlocal equations and fully nonlinear equations.

2009/11/05, Thursday afternoon session

Time: 2:00-2:40

Speaker: Seong-A Shim

Affiliation: Sungshin Women's University

Email: shims.AT.sungshin.ac.kr

Title: Bifurcation properties of Holling type predator-prey systems

Abstract: There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

Time: 2:50-3:30

Speaker: Hyundae Lee

Affiliation: Inha University

Email: hdlee.AT.inha.ac.kr

Title: Progress on the Strong Eshelby's Conjecture

Abstract: We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this train are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two linearly independent loadings the strains inside the inclusions are uniform, then the inclusion must be
of ellipsoidal shape. We then use this result to address a problem of determining the shape of an inclusion when the elastic moment tensor (elastic polarizability tensor) is extremal. We show that the shape of inclusions, for which the lower Hashin-Shtrikman bound either on the bulk part or on the shear part of the elastic moment tensor is attained, is an ellipse in two dimensions and an ellipsoid in three dimensions.

Time: 3:40-4:20

Speaker: Mikyoung Lim

Affiliation: KAIST

Email: mklim.AT.kaist.ac.kr

Title: Blow-up of Electric Fields between Closely Spaced Spherical Perfect Conductors

Abstract: The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. We establish optimal estimates for the electric field associated with the distance between two spherical conductors in n-dimensional spaces for n which is equal to or greater than 2. The novelty of these estimates is that they explicitly describe the dependency of the blow-up rate on the geometric parameters: the radii of the conductors.

Time: 4:30-5:10

Speaker: Jongmin Han

Affiliation: Hankuk University of Foreign Studies

Email: jmhan.AT.hufs.ac.kr

Title: Existence and asymptotics of topological   solutions in the self-dual Maxwell-Chern-Simons CP(1) model.

Abstract: In this talk, we consider the topological vortex equations arising in the self-dual Maxwell-Chern-Simons $CP(1)$ model. We prove the existence of solutions for any parameters $\kappa$ and $q$ by variational method. We also verify the Maxwell limit for any multivortex solutions and the Chern-Simons limit for the variational solutions. The latter limit hold true for any solutions  when there is only one vortex point and the parameters satisfy some constraints.

Time: 5:20-6:00

Speaker: Kwangseok Choe

Affiliation: Inha University

Email: kschoe.AT.inha.ac.kr

Title: Vortex solutions in the self-dual Chern-Simons-Higgs theory

Abstract: In the Chern-Simons theories, the Chern-Simons-Higgs model was proposed in an attempt to explain a certain type of superconductivity. In a static configuration, the governing equation for the Chern-Simons-Higgs model
is a semilinear elliptic equation with exponential nonlinearities, and it is often called the Chern-Simons-Higgs (vortex) equation. We briefly review recent progress on existence and asymptotic behavior for solutions of the Chern-Simons-Higgs equation.

2009/11/06, Friday morning session

Time: 9:00-9:50

Speaker: Edward Dancer

Affiliation: University of Sydney, AUSTRALIA

Email:

Title: An unexpected connection between small diffusion problems and problems with infinite boundary values

Abstract:

Time: 10:00-10:40

Speaker: Seick Kim

Affiliation: Yonsei University

Email: kimseick.AT.yonsei.ac.kr

Title: Global estimates for Green's matrices of second order elliptic systems

Abstract:

Time: 10:50-11:30

Speaker: Soo Hyun Bae

Affiliation: Hanbat National University

Email: shbae.AT.hanbat.ac.kr

Title: Singular solutions of semilinear elliptic equations and the method of phase plane

Abstract: This talk expalins how to apply the method of phase plane to classify singular radial solutions for semilinear elliptic equations with radial coefficient equipped with proper monotonicity. Particular interest is on the case involving critical Sobolev exponent.

Time: 11:40:-12:20

Speaker: Jaeyoung Byeon

Affiliation: POSTECH

Email: jbyeon.AT.postech.ac.kr

Title: Bifurcation from the essential spectrum for nonlinear elliptic problems

Abstract:

2009/11/06, Friday afternoon session

Time: 2:00-2:50

Speaker: Chang-Shou Lin

Affiliation: National Taiwan University, TAIWAN

Email: cslin.AT.math.ntu.edu.tw

Title: The minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary of domains

Abstract:

Time: 3:00-3:40

Speaker: Hyung Ju Hwang

Affiliation: POSTECH

Email: hjhwang.AT.postech.ac.kr

Title: Kinetic model in a chemosensitive movement

Abstract: Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in 1970s. The system has been shown to permit travelling wave solutions
which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this talk, we discuss a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We talk about the global existence of solutions and the existence of travelling wave solutions.

Time: 3:50-4:30

Speaker: Young-Ran Lee

Affiliation: Sogang University

Email: younglee.AT.sogang.ac.kr

Title: Exponential decay of solutions for dispersion managed non-linear Schrodinger equation

Abstract: We show that any L2 solution of the dispersion managed non-linear Schrodinger equation with zero average dispersion decays exponentially in space and frequency domains. This confirms in the affirmative Lushnikov’s conjecture of exponential decay of dispersion managed solitons. This is a joint work with M. Burak Erdogan and Dirk Hundertmark.

Time: 4:40-5:20

Speaker: Tong Keun Chang

Affiliation: KIAS

Email: chang7357.AT.kias.re.kr

Title: Mixed boundary value problem of the Laplace equation

Abstract:

Time: 5:30-6:10

Speaker: Yonggeun Cho

Affiliation: Chonbuk National University

Email: changocho.AT.jbnu.ac.kr

Title: Elliptic estimates independent of domain expansion

Abstract: In this talk, we consider elliptic estimates for a system with smooth variable coefficients on a domain $\Omega \subset \mathbb{R}^n, n \ge 2$ containing the origin. By assuming that the coefficients are in a homogeneous Sobolev space we will see an invariance of the elliptic estimates under a domain expansion

defined by the scaling $\Omega_R = \{y : y = Rx, x \in \Omega\}, R> 1$ . These invariant estimates will be applied to the existence and uniqueness of global strong solution to a parabolic system on some unbounded domains like whole space, half space or exterior domain with compact complement.

2009/11/07, Saturday morning session

Time: 9:00-9:50

Speaker: Yanyan Li

Affiliation: Rutgers University

Email: yyli.AT.math.rutgers.edu

Title: Some remarks on singular solutions of nonlinear elliptic equations

Abstract:

Time: 10:00-10:40

Speaker: Jeonhwan Choi

Affiliation: Korea University

Email: jchoi.AT.korea.ac.kr

Title: Supercritical gravity waves generated by a positive force-Theory and Experiment

Abstract: Two dimensional gravity waves of an idea fluid are studied when a positive symmetric force is given. We study KdV theory theoritically and numerically and compare the numerical results with experimental results.

Time: 10:50-11:10

Speaker: Yong Jung Kim

Affiliation: KAIST

Email: yongkim.AT.kaist.edu

Title: Asymptotic agreement of moments and higher order contraction in the Burgers equation

Abstract: The purpose of this paper is to investigate the relation between the moments and the asymptotic behavior of solutions to the Burgers equation. The Burgers equation is a special nonlinear

problem that turns into a linear one after the Cole-Hopf transformation. Our asymptotic analysis depends on this transformation. In this paper an asymptotic approximate solution is constructed, which is given by the inverse Cole-Hopf transformation of a summation of $n$ heat kernels. The $k$-th order moments of the exact and the approximate solution are contracting with order $O\big((\sqrt{t})^{k-2n-1+1/p})$ in $L^p$-norm as $t\to\infty$. This asymptotics indicates that the convergence order is increased by a similarity scale whenever the order of controlled moments is increased by one. The theoretical asymptotic convergence orders are tested numerically.