@

## 2015 N 1 22 () 15:30--16:30C16:45--17:45

kw wȍWKWOP
uҁF15:30--16:30
ikw w@wȁj
@uOn the one dimensional heat equation with a strong absorptionv
uҁF16:45--17:45

@uKorteweg-de Vries Burgers ̐isĝ܂̉̒ԋv

kw wȍWKWOP
uҁF15:30--16:30
c m ikw w@wȁj
@uϋȗ̉̍\@Ɋւāv
uҁF16:45--17:45
l ikw w@wȁj
@u僉vX̉̐v

## 2015 N 1 8 () 16:00--17:30

kw EEwȍWKWOP
u
MV isw w@wȁj
IC[̎UIƓ_QՓ˂ɂكGXgtB[U
v|
CmY̔񈳏k̂ԂɒBƂɌ铝v
͔SɌłIC[̉̐łȂƖڂɊ֌W
ĂƌĂiKolmogorov\zOnsager\zƂĒmj
݂̊֌WɂĂ̍l@[܂C܂IC[݂̑
đ傫Ȍ̐iWD̈ŁC炩łȂ
̗̉^ƂĂ̓ɂĂ͖m̕D{uł́C
IC[̎ƗvƂ̊֌WɂĂ̌̌
ЉƂƂɁCu҂ߔN݂Ă񎟌IC[
ى̗̉^ƂĂ̓ÂɊւ鐔wIElIɂ
ЉD

## 2014 N 12 18 () 16:00--17:30

kw wȍWKWOP
u
l icw wj
iq\̓s
v|
niq_̕Wɑ΂Ēꂽ̐ςƕ\ʐςsA
Us𓱂A𐬗œKȐ}͗̂Ɍ邱ƂB
ؖ͌ÓTIȓsɑ΂X. CabrẽACfAɊÂB
͑ȉ~^Δ̉ɑ΂Aleksandrov-Bakelman-Pucci
ől̏ؖ@p̂ŁA{ułNeumannEt
Poisson̉𐫂Ảɑ΂Cabre̎@pB
Cabreɂ錳X̃ACfAƁAUꍇ̔񎩖ȓ_𒆐SɉB

## 2014 N 12 15 () 14:00--15:30

kw wȐw 2K 209
u
B Ǎs iBw w@w@j
On the stability of viscous compressible flow
v|
{uł͈kNavier-Stokes̕s̈萫l@D
CmEEYу}bnꍇ̕s̈萫
̝̎ԖɂQߋɂēꂽʂ
}bnx傫Ƃ̃|YC̕s萫
ԎIisg̕ɂĂ̌ʂЉD

## 2014 N 12 4 () 16:00--17:30

kw wȍWKWOP
u

On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
v|
We are concerned with the Cauchy problem of the full
compressible Navier-Stokes equations satisfied
by viscous and heat conducting fluids in the whole space.
We focus on the so-called critical Besov regularity framework.
After recasting the whole system in Lagrangian coordinates, and
working with "the total energy along the flow" rather than with the
temperature, we discover that the system may be solved by means of
Banach fixed point theorem in a critical functional framework whenever
the space dimension is greater than two. Back to Eulerian coordinates,
this allows to improve the range of the Lebesgue exponent for which
the system is locally well-posed, compared to previous results.
This is a joint work with Raphaël Danchin (UPEC, LAMA).

## 2014 N 11 27 () 16:00--17:30

kw wȍWKWOP
u
ǎj i_ˑw w@CȊwȁj
Stability analysis of axisymmetric CMC surfaces
via surface diffusion equation
v|
\ʊgU͔4K^ΔƂĕ\
Ȗʂ̔WłCȖʂ̕\ʐςGlM[Ċ֐
EEĂ݂ƂCH^{-1}-zƂēoD܂C
͂܂ꂽ̐ςɕۂȂ\ʐςŏƂ
ϕ\ĎʁC\ʊgUɑ΂EȖʂ
ϋȗȖ(ȉCCMCȖ)ƂȂD{uł́C
\ʊgU̐萫̉͂ʂēC
ΏۂȏꍇCMCȖʂ̈萫̔ɂďqׂD
ɁC~ƃAfCh̏ꍇɂāCڂ񍐂D

## 2014 N 11 20 () 16:00--17:30

kw wȍWKWOP
u
t@l iBw MIj
pFweightn
v|
weightƂ́ANewton}܂
ȒgłA̕sϗʂłB
uł́Aweightɕtg[bNl̂p
pF͖̉@ɂĉB
܂tɁA^ꂽweight݂̂̏񂩂A
ΉpFƂ̃n~gjA

pf̋ԂɁAFrobeniusl̂̍\

Ȃ悤ȍWńAFrobeniusl̂̕RWł邱ƂB

## 2014 N 10 27 () 14:00--15:30

kw wȐwQKQOX
u
Έ@K i_ˑw w@CȊwȁj
Convergence of a threshold-type algorithm
for curvature-dependent motions of hypersurfaces

## 2014 N 10 23 () 16:00--17:30

kw wȍWKWOP
u
؁@뎟 iȑw Hwj
Motion of a Vortex Filament in an External Flow
v|
In this talk, we consider the motion of a vortex ring
under the influence of external flow. This can be seen as an
idealization of the motion of a bubble ring traveling through water,
where environmental flow is also present.

The motion is described as an initial value problem posed on
the one-dimensional torus for a closed vortex filament.
The equation of motion is a nonlinear dispersive type equation
and is an extension of the Localized Induction Equation (LIE).
The LIE is one of the most oldest and fundamental model equation
describing the motion of a vortex filament, and the equation we
consider in this talk is a generalization of the LIE which
takes into account the presence of external flow.
The time-local solvability of the initial value problem
will be presented, focusing on the derivation of
energy estimates needed in order to prove the solvability.

## 2014 N 10 9 () 16:00--17:30

kw wȍWKWOP
u
Z q ikw w@wȁj
Asymptotic behavior of solutions to a system of quadratic nonlinear Schr\"odinger equations with mass resonance
v|
In this talk, we consider the final state problem for a system of nonlinear Schr\"odinger equations with three wave interaction in two dimensions. In our previous study, we constructed a solution of a two components system which describes the mass transition phenomenon by using the hyperbolic functions. We here show that the existence of a solution of a three components system which describes the mass transition phenomenon periodically in time by using the Jacobi elliptic functions.

## 2014 N 10 2 () 16:00--17:30

kw wȍWKWOP
u
Hi Jun Choe (Yonsei University w)
A semilinear parabolic equation with free boundary
v|
@We consider non-negative solutions of the heat equation with strong absorption,
@$\partial_t u-\Delta u=-u^{\gamma} \chi_{u>0}$ in $(0,\infty) \times \Omega$,
@where $\Omega$ is a smooth bounded domain in $R^n$, $\gamma \in (0,1)$,
@and initial and boundary data are prescribed. Assuming merely regularity
@and a growth condition of the data, we prove optimal regularity and
non-degeneracy
@estimates for the solution, which already have interesting
consequences as for example
@finite propagation speed of the set $\{u>0\}$. We then show that the
@n1-dimensional Hausdorff measure with respect to the parabolic metric
is locally finite
@on the free boundary $\{u>0\}$.

@Concerning the Cauchy problem with respect to $\gamma \in (0,1)$
@we know more: any self-similar solution in $(-, 0) \times R^n$
@is either time-independent or coincides with the solution
@$U_1(t,x)=\max (0, (1-\gamma)(-t)^{1/1-\gamma}$.
@As a consequence, the free boundary can be divided into a closed set of
@horizontal points which is locally contained in an n-dimensional
Lipschitz surface and
@on which $U_1$ is the unique blow-up limit, and a relatively open set
of non-horizontal
@points on which any blow-up limit is a steady-state solution. We
proceed to characterize
@the asymptotic behavior near horizontal points.

@Finally we consider the case of one space dimension in which we
obtain that any blow-up
@limit is unique and that the regular non-horizontal part of the free
boundary is open and a
@$C^{1/2}$-surface. The last result is extended to the case of higher
dimensions in.

## 2014 N 7 24 () 16:00--17:30

kw wȍQKQOT
u
_j iw Hj
QQt@g̉̔ɕtŗLl̋Ƃ̉p
v|
QQt@ǵA^w֐ł锼ȉ~^El
łEA܂܂p[^0ɋ߂ÂƂ̍őlUꍇ

ڍׂȋ񍐂B܂E̎̉pƂāAΉŗL֐̃Ot
̊Tɂĕ邱ƂЉB
Ƃ̋iarXiv:1308.3628jɊÂB

## 2014 N 12 4 () 16:00--17:30

kw wȍWKWOP
u

On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
v|
We are concerned with the Cauchy problem of the full
compressible Navier-Stokes equations satisfied
by viscous and heat conducting fluids in the whole space.
We focus on the so-called critical Besov regularity framework.
After recasting the whole system in Lagrangian coordinates, and
working with "the total energy along the flow" rather than with the
temperature, we discover that the system may be solved by means of
Banach fixed point theorem in a critical functional framework whenever
the space dimension is greater than two. Back to Eulerian coordinates,
this allows to improve the range of the Lebesgue exponent for which
the system is locally well-posed, compared to previous results.
This is a joint work with Raphaël Danchin (UPEC, LAMA).

## 2014 N 7 17 () 16:00--17:30

kw wȍQKQOT
u
 i_ˑw wȁj
ԎIpXł̗ʎqU
v|
Qʂɑ΂AԎIpXɒ

ꂪĂȂ΁A̗q̉^͎R^ƂȂB
ł́ÃI^ItԎIɌJԂꍇɂ
ǂ̂悤ɂȂ邩AƂfpȖl@B́AP
EEE̎̃I^It̎Ԃ̒Aדdq̔dׂƁA
ÎƂ̎̋܂邠𖞂ĂƂɂ́A
q͑ΐɎOĔыĂ悤łB
̂ƂAS͂ɂۓāAU_̗ꂩ猩ĂB
{u͐{Ii_ˑwjƂ̋ɊÂB

## 2014 N 6 19 () 9:30 -- 6 20 ij17:00

W
Numerical Analysis for Partial Differential Equations
kw Ȋw 6Kc
vO
pdf t@C D

## 2014 N 6 12 () 16:00--17:30

kw wȍQKQOT
u
c iHcw 當wj
Mn̔_ɂ
v|
񐬕nM̔ƑI𐫂ɂčlB
{͕Е̐[łꍇɂ͓c^ƈv̂łB
{uł͗[łȂꍇɂ̔ɂčl@A
_̐ƈʒuǂ̂悤Ɍ肳̂ȒPȏꍇɌĐB

## 2014 N 6 5 () 16:00--17:30

kw wȍRKROR
u
@ iÉw Ȋwȁj
On estimates for the Stokes flow in a space of bounded functions
v|
The Stokes equations are well understood on $L^p$ space for various
kinds of domains
such as bounded or exterior domains, and fundamental to study the nonlinear
Navier-Stokes equations. The situation is different for the case
$p=\infty$ since in this case
the Helmholtz projection does not act as a bounded operator anymore.
In this talk, we show some a priori estimate for a composition
operator of the Stokes
semigroup and the Helmholtz projection on a space of bounded functions.

## 2014 N 5 15 () 16:00--17:30

kw wȍRKROR
u
JEVhJ iw Hj
oȌ^RE̋ߎ\ɂ
v|
oȌ^pfɑ΂鎩RE͉͓IʂقƂǓĂȂVQłD
{uł́Cߎ̋ɌƂĉ\ʓIȕ@ĂC1̏ꍇ
̕@ŉ邱ƂD͂͐ΌȂǂ̖ʏ^
ۂ̃fƂĉp邽߁CɈ͂܂̐ςɑ΂S̉eɂĂlD

## 2014 N 5 8 () 16:00--17:30

kw wȍRKROR
u
S (cw iHw)
L^p - ^̃mlɑ΂VfBK[̉𐫂ɂ
v|
{uł͔VfBK[̏lɂāA֐ L^p - Ԃ
ގ̊֐ԂɂꍇɁẢ𐫂ɂčl@B߂ɏl̃NXƂ
L^p - ԂlAVargas Vega (2001) ̃ACfA𗘗p p 2 ɏ\߂Ƃɑ
݂鎖Bɏ֐̋ԂƂL^p-Ԃ̑ɁApϕȊ֐ԂƂĂׂA
L^p ɋ߂Ԃ𓱓A̋Ԃɑ΂ĔVfBK[K؂ƂȂĂ鎖B

## 2014 N 4 24 () 16:00--17:30

kw wȍRKROR
u
O ^m (kw w@w)
Invariant sets of nonlinearly perturbed Keller-Segel system of parabolic-parabolic type with critical degenerate diffusion
v|
Keller-Segeln, זESۂ̑ɂWۂLqfł,
זESۂ̌̖xƔSۂU鉻w̔Zx𖢒m֐Ƃ
^Δł. őƂ, Sۂw̔ZxTm,
Zxz̍ɓ. {uł, SۂU鉻wꎩg
Zxׂ̂ɔႵĐl@, ԑ݂邽߂̏\^.

## 2014 N 4 17 () 16:00--17:30

kw wȍ`RKROR
u
O ב (kw w@w)
On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem
v|
In this talk we discuss the space of solenoidal vector fields in an unbounded domain
$\Omega\subset \R^n$, $n\geq 2$, whose boundary is given as a Lipschitz graph.
It is shown that, under suitable functional setting, the space of solenoidal vector fields is
isomorphic to the $n-1$ product space of the space of scalar functions.
This result reveals a generic structure for the Stokes operator and the associated semigroup.
Our result also covers the whole space case $\Omega=\R^n$.
This talk is based on a joint work with Hideyuki Miura (Tokyo Institute of Technology).