@

## QOOVNRW@16:00--17:00

u
Hyungjin Huh (s )
On the initial value problem of the Chern-Simons-Higgs equations

u
쎛 L ik j
Hele--Shaw ɂ鎩RE̋

## QOOVNPQQ@13:20--15:30

uҋyё
u
13:20?14:20
uҁF|c u ik j
ځFU^g݂̉̑Ɣ񑶍݂ɂ

u
14:30?15:30
uҁF͌ _ (k )
ځFAJvbgIvVɑ΂鉿it̉̋\

uҋyё
u
15:30?16:30
uҁF i (k )
ځFEE^ɑ΂鐳]ɂ

u
16:40?17:40
uҁFR{ @ ik j
ځFڗgỦ̋

## QOOVNPPT@13:20--15:30

uҋyё
u
13:20?14:20
uҁF Fh ik j
ځFϕsp Korn ̕s̓o

u
14:30?15:30
uҁFaq ik j
ځFKeller--Segel ñXP[sςȋԂɂ݂̑ƈӐɂ

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

u
n (k , Ɍ)
ȃXyNgMbvԂ̒fMJڊm Stokes 􉽂ɂ
v|
Ώ̂ 2~2 sn~gjAƂ ԈˑVfBK[lD Q̎ŗLlԂɃMbvꍇɂJڊmɂāC fMp[^Ƃ̃XyNgMbv\p[^ ɂOɋ߂ÂƂ̑Qߋ𒲂ׂD ʂɑJڊm̒fMɌ́CwIɌ邱ƂmĂD ɂ̎v́CŗLl̕fʏ̌_iς_j ʂStokesȐɂētD uł́C̕ς_̈_Ɏꍇɂ Jڊm̑QߌЉD ɂ̎vyь덷CQ̃p[^ ֊֌Wɂǂ̂悤Ɉˑ邩ɂāC exact WKB@̗ꂩStokesȐ̊􉽊wI\pĐD

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

u
m ( H)
Critical frequency  Schr\"odinger multi-peak
v|
̔ȉ~^ِ̓ۓl. $$-\epsilon^2 \Delta u +V(x)u= u^p, u>0 \hbox{in}\ \R^N, @@u\in H^1(\R^N).$$ psuperlinear, subcritical̏𖞂, |eV֐V(x) 񕉂̗LE$C^1$֐$\liminf_{|x|\to \infty}V(x)>0$𖞂Ƃ. ł, V(x)critical frequencyEƌĂ΂ $\inf_{x\in\R^N}V(x)=0$Ƃ𖞂Ƃl. ̂ƂV(x)̒l܂0ƂȂkV(x)̋ɏ_ɏW multi-peak݂邱ƂϕIȃAv[ɂĎ. , multi-peak̊epeak$\epsilon$ɊւĈقȂXP[.

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

u
aco G (k )
Besov Ԃ Triebel-Lizorkin Ԃɂ Gagliardo-Nirenberg ^ԕs̗ՊEP[Xɂ
v|
̍u̖ړÍCCĎBesovԂ܂͐ĎTriebel?LizorkinԂɑ΂Gagliardo?Nirenberg^ԕsӖsharpȒ萔ƋɓƂłD̋Ԃ́CLittlewood?PaleyɂĒꂽĎSobolevԂĝłĎʁCՊEBesovԂ܂Gagliardo?Nirenberg^sƂłD܂CšnƂėՊETriebel?LizorkinԂɑ΂Gagliardo?Nirenberg^s𓾂D̕śCꂼBesovԂTriebel?LizorkinԂɑ΂ĂSobolevԂƓ悤ɁCSobolev̖藝ɑ݂̂C critical caseɂĂ͂͂CʏSobolevԂƓ\LĂ邱ƂӖĂDXɁCŎꂽ Gagliardo?Nirenberg^ԕsp邱ƂɂāČnƂĊeXɑTrudinger^sΐ^sł Brezis?Gallouet?Wainger^sD

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

u
FV (k )
LËɂ Navier-Stokes ̎̐ɂ
v|
Navier-StokesLËAɋERpNgłȂ̈ɂčl, ԉɂ̐藝ɂďqׂ. ؖɂďdvȍő吳藝(maximal regularity)ƕ(partial regularity)ɂĂЉ.

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

u
T (L )
z^weNjbNOɑ΂鐔l؂ƕΔւ̉p
v|
͊wnɌz^weNjbNO̐xۏؕtlvZ ւčusD̓Iɂ 1. jRt֐pz^weNjbNOݏؖ@ 2. ConleywpweNjbNOݏؖ@yсC̕Δւ̉pɊւ邱܂ł̌ʂ񍐂D

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

u
Marek Fila (Comenius University)
Convergence to a singular steady state of a parabolic equation with gradient blow-up
v|
We study solutions of a parabolic equation which stay bounded but their spatial derivative blows up in finite time. After gradient blow-up, the solutions can be continued in a natural way. We discuss results on the behavior of the continuation on the lateral boundary where thesingularityoccurs and on the rate of convergence to a singular steady state. This is a joint work with J. Taskinen and M. Winkler.

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

u
u (k )
O͍܂ޔ^ȉ~^̐l̑d݂ɂ
v|
{uɂĂ, $\R^n$ ̔^ȉ~^ $$-\Delta u+u=g(u)+\kappa f_0, u>0 \mbox{ in }\R^n, u(x)\to 0 \mbox{ as }|x|\to\infty$$ ɂĈ. , $f_0$ ͔񕉒lL Radon xł, $\kappa$ 𐳂 parameter Ƃ. ^ $g$ ɂĂ, (a) $g(s)=s^p$ ($1p(n+2)/(n-2)$) ܂ (b) $g(s)=as^{\beta+1}/(1+s)^\beta$ ($a>1,\beta>0$) l. O͍ $f_0$ Kȏ݂Ƃ, LȒl $\kappa^*$ ݂, $\kappa\le\kappa^*$ Ȃ΂̖͉, $\kappa>\kappa^*$ ȂΉȂƂmĂ. ł, Mountain Pass Theorem p邱Ƃɂ, $\kappa\kappa^*$ ɑ΂ďȂƂ2݂̉邱Ƃ. (b) ̂悤 1̔^lꍇ, ΉĊ֐ɑ΂ Palais-Smale ̗LEƂ. ł͎, ̍邽߂̐V@ɂĉE.

## QOOUNPOOT@16:30--18:00

u
H (l )
$\R^N$ɂ邠ȉ~^ɑ΂镄ω̑dݐ܂މ̑ďʂɂ
v|
̍uł́A$\R^N$ɂȉ~^ \begin{equation*} \label{original-problem} \left\{ \begin{aligned} -\Delta u + \mu u &= Q(x)|u|^{p-1}u \qquad\text{in $\R^N$,} \,\\ u &\in H^1(\R^N) \end{aligned} \right. \end{equation*} . A$\mu>0$, $N \geq 3$, $1 p (N+2)/(N-2)$łA $Q:\R^N\rightarrow \R$ ͓Kȏ𖞂LEA֐ł. $Q$̉ł̋ől_݂̑Ȃǂ肷邱ƂɂA ̉̑̕d݁Aɕω̑d݂ɂĂ ʂ邱Ƃ.

## QOOUNVQT@16:15--17:30

u
Laurent DiMenza iUniversite Paris-sud Orsayj
Numerical computation of solitons in nonlinear optics

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

u
Rc (k )
ٓ_ɏȖʂ̑ݒ藝ƒP
v|
􉽊wIx_ő݂񑩂Ăٓ_ɏȖ ݂̑𒲘aʑ̉pgĂ݂̏ؖ.܂ʐς̋ɏ 瓱oBlow-up͂̉pƂĂ̒PЉ.

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

u
(s )
Toeplitz operator on parabolic Bergman spaces
v|
xO}Ԃ́AƂƁAfʂ̒Pʉ~̐ ֐ŁAQϕȂ̑Ŝ̂Ȃ֐ԂƂēAn [fBԂƂ֘AȂ甭WĂ.܂A֐͒a ֐ł邱ƂAaxO}ԂRɍl邪A ɂPONقǂ̊Ԃ W.Ramey B.Choe, H.Yi ؍̐l ɂĔԏ̒axO}Ԃ̌s悤 ɂȂĂ.ł́Å֘AA|EeV_Iɂ ̂^ $(\partial_t + (-\Delta)^\alpha)u = 0$ ̉ɊւxO}Ԃl@.܂AĐjAoΐ ǂ̊{IȐmFAToeplitz pf̗LER pNg Carleson xƂ̊֘Aɂďqׂ.

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

u
Jason Metcalfe (JtHjAwo[N[Z)
Quasilinear wave equations in exterior domains
v|
In this talk, we shall discuss some recent results, obtained in part in collaborations with M. Nakamura, C. D. Sogge, and B. Thomases, on long-time existence of quasilinear wave equations in exterior domains. In three dimensions, we shall survey both almost global existence results and global existence when there is a null condition. Generally, we show that the existence of a local energy decay for the linear equation is the only geometric assumption on the obstacle which is required. With some variations on the techniques, we may also obtain similar results for elastic waves and for wave equations with localized dissipations.

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

u
G (}g w)
Lifespan ̑Qߕ]猩 Schr\"odinger
v|
$e$ p[^[ ƂāA傫 $e$̊炩ȏlɑ΂ VfBK[̊炩ȉ̍ő呶ݎԂ$T(e)$ Ƃ. Q[WsϐR̍łꍇA$e^2 \log T(e)$ Ƃʂ$e \to +0$ ɂ鉺Ɍł邱Ƃ͂悭m . {uł͂̉Ɍ̐ȕ]^A牽킩邩 c_.

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

u
Y (_ˑ H)
Blowup rate of solutions for a semilinear heat equation with Sobolev critical nonlinearity
v|
We consider the blowup rate of solutions for a semilinear heat equation with Sobolev critical power nonlinearity. First we investigate the profiles of backward self-similar solutions by making use of the variational methods and ODE arguments. Then, as an application we derive the blow-up rate of solutions, assuming the positivity of solutions in backward space-time parabola. In particular, we will try to show the existence of the so called type II blowup solutions for the Cauchy-Dirichlet problems on suitable assumptions.

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

u
Speaker: Linghai Zhang (Lehigh University, USA)
Speeds of traveling wave solutions of some nonlocal equations
v|
Different biophysical dynamic processes, mechanisms and phenomena are usually represented by different model equations (ordinary differential equations, reaction diffusion equations, and integral differential equations). These models generate traveling waves with different speeds. Our purpose is to compare the wavespeeds and steepness of the waves. We will use the general nonlocal model u_t + u = ( \alpha - \beta u) \int_{\mathbb{R}} K(x-y) H ( u ( y, t - \frac 1c |x-y| - \theta ) \, dy, where K is a kernel function, H stands for the Heaviside step function. The parameters c, \alpha, \beta and \theta are positive, each represents some biological mechanism.

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

u
Peter PolacikiSchool of Mathematics, University of Minnesotaj
On the existence and applications of exponential separation between solutions of parabolic equations
v|
It is becoming a well established fact that in general (time-dependent) linear second order parabolic equations positive solutions exponentially dominate sign-changing solutions. We will give some perspectives on such exponential separation results, in particular relate them to Harnack inequalities, and discuss some applications in nonlinear parabolic equations.

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

u
rc K (k )
On global bounds of some semilinear parabolic equations involving the critical Sobolev exponent: from variational point of view
v|
d͊ł͈lɎ_fA lɒ΂ĂRĂ͕KlɐisȂ. ̌ۂfgUnlA ̑݁AӐA܂ԑIȉ̋ɂďqׂ.

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

u
} ( VXeHwށEwn)
Ginzburg-LandaũQ[Wsςȕ]ɂ ---Q̉͂ɂނ
v|
ۂ̃fł鎥Ginzburg-Landau gaugesϐƂ傫ȎRx.݂̑ӐARegularity Ȃǂ͓̉IȐ𒲂ׂƂARxc܂܂̂邱Ƃ͑ ꍇŁAʏ킢gaugeƂt̎Rx 菜ċc_Ă.@ @̕Ɋւ镨IȊϑʁidAxȂǁj̓Q[Ws ȗʂłAɊւ萫IȐgaugeۂȂŐ ƂȂƍlĂ. @{ł́AgaugesςȗʂɊւ邢̊֌W𓱂AQ Ă΂̋ߎ̍\݂.

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

u
Joerg Wolf (Humboldt w)
On the local pressure method and its application in mathematical theory of incompressible viscous fluids

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

u
Γn ʓ (k )
On global bounds of some semilinear parabolic equations involving the critical Sobolev exponent: from variational point of view
v|
Məp^̔, Fujita^̔^ , ̒PȌEɂւ炸X̋[wI\ ƂmĂ.{uł, LË 0-Dirichlet E ۂꍇ,ԑ $L^\infty$-LEɂ l. `̎wSobolev̈ӖŗՊȄꍇɂ͂̂悤 LE͂悭mĂ邪, ՊȄꍇɂ͂̗Ⴊm Ă݂̂ł. ł, ̎XP[ϊsϐƕϕ @IȊϓ_, LE藧߂̈̏𓱂, Ă̗𓝈IɈ邱Ƃ񍐂.