The MathNet Korea
Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

고려대학교 수학과 세미나

고려대학교 수학과 세미나

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

2018 고려대학교 수학과 Colloquium

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

POSTECH IBS-CGP Seminar

2018 서울대학교 수리과학부 세미나

In many applications, the dynamics of gas and plasma can be accurately modeled using kinetic Boltzmann equations. These equations are integro-differential systems posed in a high-dimensional phase space, which is typically comprised of the spatial coordinates and the velocity coordinates. If the system is sufficiently collisional the kinetic equations may be replaced by a fluid approximation that is posed in physical space (i.e., a lower dimensional space than the full phase space). The precise form of the fluid approximation depends on the choice of the moment-closure. In general, finding a suitable robust moment-closure is still an open scientific problem. In this work we consider two specific closure methods: (1) a regularized quadrature-based closure (QMOM) and (2) a nonextensible entropy-based closure (QEXP). In QMOM, the distribution function is approximated by Dirac deltas with variable weights and abscissas. The resulting fluid approximations have differing properties depending on the detailed construction of the Dirac deltas. We develop a high-order discontinuous Galerkin scheme to numerically solve resulting fluid equations. We also develop limiters that guarantee that the inversion problem between moments of the distribution function and the weights and abscissas of the Dirac deltas is well-posed. In QEXP, the true distribution is replaced by a Maxwellian distribution multiplied by a quasi-exponential function. We develop a high-order discontinuous Galerkin scheme to numerically solve resulting fluid equations. We break the numerical update into two parts: (1) an update for the background Maxwellian distribution, and (2) an update for the non-Maxwellian corrections. We again develop limiters to keep the moment-inversion problem well-posed. The work on the regularized quadrature-based closures is joint with Erica Johnson (Bexar County) and Christine Wiersma (Iowa State), and the work on the nonextensible entropy-based closures is joint with Chi-Wang Shu (Brown).

2018 서울대학교 수리과학부 세미나

In this talk, we study the Taylor spectra between a spherical Aluthge transform of spherically quasinormal pair and its original pair.

2018 서울대학교 수리과학부 세미나

We consider a multi-phase energy functional whose ellipticity rate and growth radically change according to variable coefficients. The aim of the talk is to show the Hölder regularity for the gradients of local minimizers of the multi-phase energy functional under sharp assumptions relating the growth couples to the Hölder exponents of the modulating coefficients. The talk is based on the joint work with Cristiana De Filippis (Oxford).