@

## QOPONPQW@15:00--17:35

uҋyё
u
15F00?15:45
uҁFz (kww@ w)

u
15:55?16:40
uҁF [ (kww@ w)
ځFg̒ԉ݂̑ƊÖɂǏGlM[̌]ɂ

Ou
16:50?17:35
uҁFēc Fz (kww@ w)
ځFgqsqdd^̏lɂ

## QOPONPQP@15:00--17:35

uҋyё
u
15F00?15:45
uҁFHc q (kww@ w)
ځFזE̐䃂fɂ̑

u
15:55?16:40
uҁF쌎 Y (kww@ w)
ځFgJƃ{eɂߐHҁEHҌn̗͊wI\ۂUf̉

Ou
16:50?17:35
uҁF{ O (kww@ w)
ځFώ}̂ɂ锽gUJjYɂg̓d

## QOPONPPS@15:00--17:35

uҋyё
u
15F00?15:45
uҁFBenoit Thang-Long Pham-Dang (kww@ w)
ځFEconomic Equilibrium in an Information-based Framework

u
15:55?16:40
uҁF z (kww@ w)
ځFM̉̔Ẅʒu̓t

Ou
16:50?17:35
uҁFF (kww@ w)
ځFDȔ^̑̕

## QOOXNPQPO@16:00--17:30

u
Clement Gallo (Universite de Montpellier)
On the Thomas-Fermi ground state in a harmonic potential.
v|
We study the ground state of the Gross-Pitaevskii equation with a harmonic potential, $$iu_t+\epsilon^2\Delta u+(1-|x|^2-|u|^2)u=0, (t,x)\in \R\times \R^d,$$ in dimensions d=1,2,3, in the semi-classical limit $\epsilon\to 0$. Using solutions of the Painleve-II equation, we give an asymptotic expansion of the ground state in the semi-classical limit, that justifies the Thomas-Fermi approximation. In the space of one dimension, we use this characterization of the ground state to describe the behaviour in the semi-classical limit of the eigenvalues of a Schrodinger operator associated with the ground state.

## QOOXNPPQU@16:00--17:30

u
ɓ T (dCʐMw dCʐMw ʐMHw)
񓙕eɂKChg̉
v|
ώȔ񓙕e(̒êɋ܂Ăꍇl)̒dg̐Aɂ̕U֌W(gƓdx̊֌W)̑Qߋ𒲂ׂ.ê̏ꍇ͍HwIɏdvł悭ׂĂ邪A񓙕̏ꍇɂĂ̈ʓIȌʂ͂قƂǂȂ.wI͂̓p[^tslpfɑ΂ŗLlɋA.ʂɂ͒Pq_̌tAȖ(̐؂)̊􉽂ɑΉ邱Ƃł.

## QOOXNPPPX@16:00--17:30

u
Marek Fila (Comenius University, Slovakia)
Stabilizing effect of diffusion and Dirichlet boundary conditions
v|
It is known that diffusion together with Dirichlet boundary conditions can inhibit the occurrence of blow-up. We examine the question how strong is this stabilizing effect for reaction-diffusion equations in one space-dimension. We show that if all positive solutions of an ODE blow up in finite time then for the corresponding parabolic PDE (obtained by adding diffusion and the Dirichlet boundary condition) there is either an unbounded sequence of stationary solutions or an unbounded time-dependent solution.

## QOOXNPPPQ@16:00--17:30

u
^ (kww@ Ȋw)
2SԂɂSchrodinger-Poissonn̉
v|
Schrodinger-Poissonn2ōl.̕n͔^Schrodinger̓T^̈ŁA3ȏ̏ꍇ͈ʘ_ɂ舵Ƃł. 2lł̑傫ȏQPoissonł. Newton|eVɂPoisson̉^ɂ͈Ȍ̉͂ɕssȏKvȂ̂ŁAアŒł𓱓.^̉ł̔Uۓ@pĉƂȂ̂ŁAʎq̂̕ɋAƂ@pĉ͂.

## QOOXNPPT@16:00--17:30

u
(kww@ w)
ԂɂEtM̑̕
v|
{uł͔˂̕Iȉ߂̂PƂčlĂEtM̏Ell. ^̐l̑拓ɂĂ͂܂łlXȎ@ɂ葽̌sĂ, EtM,̑拓ɂĂ͔ԂłقƂǌʂĂ炸,̌ʂƂĂ, c^Ɠl,wɂĎԑ̑ݔ񑶍݂ω邱ƂmĂ݂̂ł. {uł͔ԂɂEtM̐lɑ΂ĔM̉ɑ΂錋ʂƓľʂ𓾂邱ƂڕWƂ. Ȃ{u̓e͓kw̐ΖјaOƂ̋ɂ̂ł.

## QOOXNPOPT@16:00--17:30

u
Hermann SOHR (Univ. Paderborn, Prof. emirtus)
Recent results on weak and strong solutions of the Navier-Stokes equations
v|
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain. This condition is not only sufficient - there are several well-known sufficient conditions in this context - but also necessary, and yields therefore the largest possible class of such strong solutions. As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.

## QOOXNPOW@16:00--17:30

u
(wbHw)
Degenerate parabolic equation with critical exponent derived from the kinetic theory
v|
We consider a degenerate parabolic equation derived from the kinetic theory. Existence of the weak solution, the threshold mass for a solution blowing up in finite time, $\varepsilon$-regularity, and the structure of the blowup set are studied. Some similarities and differences between our equation (in higher space dimensions) and the Smoluchowski-Poisson equation in two-space dimensions arise.

## QOOXNVPU@16:00--17:30

u
^ (wlЉȊwȊwے)
ȐŒꂽ鎞Ĕɑ΂ϕ
v|
We consider a variational problem for a certain space-time functional defined on planar closed curves. The functional appears in an action minimization problem for stochastic Allen-Cahn equation. The variational problem is stated as follows: Let $\Gamma_0$ and $\Gamma_1$ be given planar closed curves and $T$ be a given positive constant. Then minimize the space-time functional over family of planar closed curves, which deform from $\Gamma_0$ to $\Gamma_1$ in time $T$." In this talk, we focus on an existence of non-radially symmetric critical point of the variational problem, in particular a solvability of an initial final value problem.

## QOOXNVQ@16:00--17:30

u
x aO (kww@wȐwU)
No-fattening criterion for Brakke motion
v|
In the talk, we propose a sufficient condition for Brakke motion to have no-fattening. Brakke motion is a weak solution on Mean curvature motion. The definition involves a few terms from Geometric measure theory. After I mention them, I point out pros and cons for Brakke motion in contrast to other weak-notion on Mean curvature motion. Next we briefly introduce a work by T.Ilmanen, which has constructed a Brakke motion as the singular perturbation limit on the solution of Allen-Cahn equation. In the latter, I present an improvement of his idea and I discuss what condition makes it nofattening.

## QOOXNUQT@16:00--17:30

u
] (s喼_)
Resolvent estimates for magnetic Schr\"odinger operators and smoothing effects for related evolution equations
v|
$\Omega\subset{\bf R}^n$ ($n\geq 3$) starshaped ȋEÖƂ, Schr\"odinger $$-\Delta_bu+c(x)u-\kappa^2u=f(x), u|_{\partial\Omega}=0$$ l. , $\Delta_b=\nabla_b\cdot\nabla_b$, $\nabla_b=\nabla+ib(x)$, $b(x)=(b_1(x),\cdots,b_n(x))$ ł. $\nabla\times b(x)$, $c(x)$ ĉ $O(r^{-2}$ ̌Ƃ, $L=-\Delta_b+c(x)$ resolvent $\kappa\in \{\bf C}_+$ ɑ΂l]߂. ܂, ̉pƂĔWpf $$e^{itL}, \quad e^{it\sqrt{L+m2}} \ \ (m\geq 0)$$ ̎ł̏d݂ $L2$ ] (smoothing effect) .

## QOOXNTQW@16:00--17:30

u
lG (kww@wȐwU D2)
ĎEɂNavier-Stokes̎Ԏɂ
v|
{uł͔ĎEۂNavier-StokeslAO͍ԎIȏꍇɓyы݂̑.- VɂA\mC_xNg͒aƉ]ɕłAa̐䂪̍\ɂďdvł邱Ƃꂽ.ŋEl̃\mC_gꂽ֐̒a𐧌䂵\AԎ̈ʉłreproduct propertyƂЉ. ܂AEl̃g[Xmꍇɂ́Â܂ŁAԎIȋNavier-Stokes̏ƂđAۓpfLE͓IQɑ΂$L^p$-$L^q$^]^邱Ƃō\ł邱ƂЉ.

## QOOXNTQP@16:00--17:30

u
J VhJ (w@Olʌ)
ϕSt̎REWΔɂ
v|
uł́A̐ϕۑɂǏIȍƎRE^.ŏɁA\ʒ͂dIl@ƂɁAʏɂtH̋f_̕𓱏o.ɕ݂̉̑Ȃǂ̉͂s.̐ςEɕۂƂS߂ɁA𔭓WɓKꂽŏƂĕ\.IɁAݎgł֘AƐlvZɊւăRgAvZʂЉ.

## QOOXNTPS@16:00--17:30

u
G (xRwHw)
-gȖݍpƑމgUCgUƂ̊֌W
v|
Xet@CE}̗Ƃމ^n␔ԊwɌgUnȂǂ̂悤ȁCgU܂ނ܂܂Ȗ舵.̉CgUł锼gUnɂߎ邱Ƃ.̂Ƃ́CgUnɔׂĊiiɖLxȍ\ĂƎvމgUgŨJjYC͐gUƒPȔ̑ݍpɂčČ邱ƂĂ.

## QOOXNTV@16:00--17:30

u
z (kww)
Blow-up for a semilinear parabolic equation with large diffusion of ${\bf R}^N$
v|
{uł, SԂɂĔM̊gUW\傫ꍇl. gUW\傫Ƃ, gǓʂ, Ẅʒutɂ͔M̉̎ԑI\ĂƂƂЉ.

## QOOXNSQR@16:00--17:30

u
V S (kww@w)
ϐSWXg[NXpfƂ̗̗͊wւ̉p
v|
SWԂ̊e_Ɉˑĕω悤ȃXg[NXlƁCɕtāCXg[NXpf̗ގlCꂪ͔Q𐶐C$H_{\infty}$-calculus ƂƂ.l̈́CLËyъÖyѐۓw܂ނNX̔LËŁC̈̊炩͒ႢꍇlCEƂẮCDirichlet-Neumann yт̍El.ɁCԔWϐSWXg[NX L^p ő吳]ꂩ瓱oł邱ƂC̕]pāC̉^LqgUEf̕܂ނ悤ȈʓIȗ̕ɑ΂āCԋǏ݂̑ L^p Ԃ̘gg݂ŏؖł邱Ƃ.

## QOOXNSPU@16:00--17:30

u
|c u (kww@w)
AU^g̎ԑɂ
v|
AU^g̏lɑ΂鎞ԑ̑݁A񑶍݂肷̙p̏(ՊEw)ɂďqׂ. U^g̉́AԑIɐM̉ɑQ߂APƂ̔U^g̏ꍇA̗ՊEw͑ΉMƈv.ɑ΂A{uł́AԂŌ݂ɈˑAn̗ՊEwAΉ`Mn̗ՊEwƈv邱Ƃɂďqׂ.