Titles and Short Summaries of the Talks

43 Functional Equations
Final: 2013/2/7
26 Yusuke Kotera (Osaka Univ.) ♯ Hadamard variational formula for general domain perturbation · · · · · · 10
Takashi Suzuki (Osaka Univ.)
Takuya Tsuchiya (Ehime Univ.)
Summary: We study the Hadamard variational formula for general domain perturbation, especially
second variational formula for Dirichlet problem and mixed problem.
27 Yoichi Miyazaki (Nihon Univ.) ♯ Lp regularity theorem for elliptic equations and smoothness of the
domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We derive the Lp regularity theorem for elliptic equations under restricted smoothness
assumptions on the boundary of the domain. If the elliptic operator is of order 2m, we can lessen the
smoothness assumption by m − 1 in both cases of non-divergent operators and divergent operators.
13:30–14:30 Award Lecture for 2012 Analysis Prize
Shigeru Sakaguchi (Tohoku Univ.) ♯ Stationary isothermic surfaces and geometry of domain
9:30–12:00
Summary: This talk is based on the results obtained by collaborating with Rolando Magnanini
(Università di Firenze). Let Ω be a domain in R N (N ≥ 2) with ∂Ω = ∂ ( R N \ Ω ) . We consider the
solution u of either the initial-boundary value problem, where the initial value equals zero and the
boundary value equals 1, or the Cauchy problem where the initial data is the characteristic function
of the set R N \ Ω. A hypersurface Γ in R N is said to be a stationary isothermic surface of u if at
each time the solution u remains constant on Γ. The problem we consider is the classification of all
the domains Ω having a stationary isothermic surface. We review the previous results and report
some new results. Among these, in particular, a new result concerning the characterization of the
circular cylinder in R 3 is reported.
March 22nd (Fri) Conference Room IV
28 Chihiro Aida
Chao-Nien Chen
(Meiji Univ.) ♯ Diffusion-induced bifurcation from infinity · · · · · · · · · · · · · · · · · · · · · · · · 15
(Nat. Changhua Univ. of Edu.)
Hirokazu Ninomiya (Meiji Univ.)
Summary: Diffusion term has an influence on global existence of solution in reaction diffusion
system. It is known that there is this phenomenon in some specific nonlinearity, however, how do
we understand this phenomenon in the case of general nonlinear term? In this presentation I will
explain diffusion-induced bifurcation from infinity as one of answer to this question.
29 Yuki Kaneko (Waseda Univ.) ♯ Spreading and vanishing for free boundary problems in an ecological
Yoshio Yamada (Waseda Univ.)
Kazuhiro Oeda (Waseda Univ.)
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider free boundary problems for reaction-diffusion equations modeling the
spreading of species, where unknown functions are population density and spreading front of
species. Moreover, the dynamical behavior of the free boundary is determined by Stefan-like
condition. The purpose of this talk is to show the asymptotic behavior of solutions which is
understood as dichotomy theorem of spreading or vanishing of species. We also give some sufficient
conditions for spreading or vanishing.