@

## QOORNPPU@13:30--17:00

uҋyё
u
15:30?16:30
uҁFx (k )
ځFAJvbgIvVɑ΂ubN-V[YƑsgE̋

u
16:40?17:40
uҁFRc ^ (k )
ځFՊEp`ɂ`g̉̐ Wave Map ւ̉pɂ

## QOORNPX@15:30--17:40

uҋyё
u
15:30?16:30
uҁF (k )
ځFd݂`gU̒̈萫

u
16:40?17:40
uҁF{ (k )
ځFChafee-Infante ^Elɂ̕

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

u
Irina Kozlova (Swinburn University of Technology)
A Numerical Study of Modelling in Mathematical Biology
v|
Reaction-diffusion systems have been playing an important role in the understandin of various phenomena arising in mathematical ecology. The main theme of this lecture is an effort to understand the biological process of predator-prey systems through numerical simulations. Here we focus on three different problems of mathematical ecology using the operator splitting methods. First, the two-dimensional spruce budworm models are considered under the assumptions, one with density dependent diffusion balanced by an artificial wind equal to the population gradient and the other with density dependent diffusion in the absence of wind. The effects of initial and different hostile boundary conditions have been investigated in this problem. Next, predator-prey models based on Luckinbill's laboratory experiment with Didinium nasutum and Paramecium aurelia are considered with the inclusion of time delay and spatial dependence through diffusion. In this problem, effects of the initial conditions, functional response, diffusion and time delay terms on the solutions of predator-prey equations are investigated. Next, numerical simulations of the population dynamics of twospotted spider mite Tetranychus urticae and its predator Phytoseiulus persimilis on carnations have been carried out. This study is based on the field data obtained from the Institute for Horticultural Development, Knoxfield, Victoria, Australia. A new method to obtain intrinsic growth rate of prey population dependent on temperature has been developed. The parameter estimation for the temperature dependent predator-prey models has been carried out with the inclusion of diffusion and time delay. It has been shown that the inclusion of temperature in the models has improved the results of the best fit of solutions to the field data. A possible strategy for the biological control of the pest population based on the temperature dependent simulation models has been developed.

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

u
c vj (s )
xNg@̔WƏ^g̎ԑ
v|
u~RtXL[ԂKilling xNgp\{t^sƁÃxNg gpfi_x[VAj̉ƂA^\$Box u=0\$̉̎ł ]GlM[̊ȒPȌvZ瓱B̔zKpāAKlainerman ^g̏ĺAȃf[^ɑ΂鎞ԑ𐫂̗_𔭓WB @A^oȌ^̑\ł^e̕∳kIC[ ͂ɂẮA~RtXL[ԏŒ`ꂽʑƂ݂ȂKlainerman̕@𒼐 Kp邱Ƃ͂łȂB܂̖ƂĔgQ̊Oŉ͂邱Ƃ [B̂悤Ȗl@邽߂ɂLorentz boostƂ΂xNgpȂ@ ̍\zsƂȂB Z~i[ł́AKlainerman--SiderisɂčlĂꂽ@i邱ƂɂAKlainerman 藝ɕʏؖ^邱ƂɐGB܂AԋǏ̃AvI]ɗpmɊ܂܂ XP[OIy[^(tpartial_t+xcdotnabla)̌ɒӂƁAŋ߂Keel--Smith--Sogge ɂAԂȐꍇ``Almost Global''ȉ̑ݒ藝ɊȒPȕʏؖ^邱Ƃ GB̍l@́AԂRŗLEȐ^Q̊Oł̏lEl̉͂ 𗧂ƎvBv

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

u
ēc OY (L Ȋw)
Precise asymptotic formula for eigenvalues of semilinear elliptic eigenvalue problems.
v|
We consider the following semilinear eigenvalue problem \$\$ -Delta u + u^p = lambda u, enskip u > 0 quad mbox{in} enskip Omega, enskip u = 0 quad mbox{on} enskip partialOmega, \$\$ where \$Omega subset mbox{bf R}^N\$ (\$N ge 2\$) is an appropriately smooth bounded domain, \$p > 1\$ is a constant and \$lambda > 0\$ is an eigenvalue parameter. It is known that for a given \$alpha > 0\$, there exists a unique solution \$(lambda(alpha), u_alpha) in mbox{bf R}_+ times C^2(bar{Omega})\$ satisfying \$Vert u_alphaVert_{L^2(Omega)} = alpha\$. We establish the precise asymptotic formula for \$lambda(alpha)\$ with exact second term as \$alpha to infty\$.

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

u
NV (k )
Existence of Navier-Stokes flow in the half space with non-decaying initial data.
v|
ԂɂStokesɂĂ̂̕]ƂɁAԂɂ Navier-StokesŁAlŌȂ݂̂̉̑ƈӐB

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

u
Jong-Shenq Guo (Taiwan Normal University)
Single-point Blow-up Patterns for A Nonlinear Parabolic Equation
v|
We study a nonlinear parabolic equation with a superlinear reaction term. By studying the backward self-similar solutions for this equation, we construct a finite number of self-similar single-point blow-up patterns with different oscillations.

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

u
ЎR Y (a̎RE)
`dẍقȂ`gnɑ΂̑
v|
A̔`gnɑ΂鏉ll., Ƃɓ`dxقȂ, `m֐Ƃ̓֐̑oɈˑꍇl@̑ΏۂƂ.ȏ^ Ƃ, ԑ߂̏\^邱Ƃ, {u̎ړIł. Ԃ, lifespan ɂĂ̌ʂqׂ

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

u
v (Ej
ՊEp`Ɏ f^ Ginzburg -Landau @̑QߓIU镑ɂ
v|
http://www.math.tohoku.ac.jp/%7Esa2m17/homepage/hayashi.pdf

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

u
V V (kE)
Stability and instability analysis of critical points near sphere of the bending energy under constraints.
v|
The variational problem of the bending energy of surfaces under constraints arised in the study of the models of human red blood cell. We have already shown the existence of critical points bifurcating from the sphere and have obtained a criterion for their stability. The criterion can be directly checked for solutions of low mode (the definition of mode will be given in the talk). The higher the mode is, the more diffucult the direct calculation of the criterion becomes. In my talk I will show that by applying asymptotic snalysis we can get some detailed information about stabilty for higher mode solutions.

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

u
Marek Fila (Comenius University)
Singular connections between equilibria of a semilinear parabolic equation.
v|
http://www.math.tohoku.ac.jp/%7Esa2m17/homepage/fila.ps

## QOOQNPOPV@16:00-17:30

u
Cheng He (_ˑE)
On \$L^1\$ summability and asymptotic profiles for incompressible smooth solutions to Navier-Stokes equations in a 3D exterior domain
v|
The exterior nonstationary problem is studied for the 3-D Navier-Stokes equations. The \$L^1\$-summability is proved for smooth solutions which correspond to initial data satisfying certain symmetry and moment conditions. The result is then applied to show that such solutions decay in time more rapidly than observed in general. Furthermore, an asymptotic expansion is deduced and lower bound estimate is given for the rates of decay in time.

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

u
Jean Ginibre (University of Paris XI)
Long range scattering for the Wave-Schr"odinger system
v|
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation@with a Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the data and we determine theasymptotic behaviour in time of solutions in the range of the waveoperators. The method consists in solving the wave equation, substituting the result into the Schr"odinger equation, which then becomes both nonlinear and nonlocal in time.The Schr"odinger function is then parametrized in terms of an amplitude and a phase satisfying a transport/Hamilton Jacobi system, and the Cauchy problem for that system, with infinite initial time and prescribed asymptotic behaviour determined by the asymptotic state, is solved by an energy method, thereby leading to solutions of the original system with prescribed asymptotic behaviour in time.

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

u
Γn ʓ ( H)
Multiplicity of solutions of some semilinear elliptic equations with weight function: Morse theoretical approach

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

u
Α V (ꋴ o)
Exact pricing formulas for the American options

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

u
n Y (wK@ )
Maxwell ܂ Stokes ̉̊Eʐ

u
Y (k )
OKU^̏l̓Kؐ

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

u
qc a_ (s )
Symmetry breaking in an optimization problem for a nonlinear elliptic BVP

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

u
Hc r (V H)
The nonstationary Stokes and Navier-Stokes flows through an aperture

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

u
gA (k )
Singular perturbation problems with surface tension