Titles and Short Summaries of the Talks

47 Functional Equations
9:30–11:45
March 23rd (Sat) Conference Room IV
Final: 2013/2/7
46 Hiroyuki Takamura
∗ An example of dissipative structure of nonlinear wave equations with
(Future Univ.-Hakodate)
Kyouhei Wakasa
(Future Univ.-Hakodate)
quadratic terms in four space dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: One of the final problems which was open more than 20 years on the optimality for the
general theory of the fully nonlinear wave equations was solved by our previous work (J. Differential
Equations, 2011). Such a result is achieved by so-called almost global solution of a semilinear
equation with a single and positive quadratic term in four space dimensions. In this talk, I would
like to show you another equation with a special quadratic term of non-single and indefinite sign
which admits a global in time solution.
47 Kazuyuki Doi (Toyama Pref. Univ.) ∗ On the weighted pointwise estimates for derivatives of solutions to the
Hideo Kubo (Hokkaido Univ.) wave equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we would like to present a simplified approach to the weighted pointwise
estimate for the solution to the inhomogeneous wave equation in three space dimensions obtained by
the work of Yokoyama (2000). Actually, we are able to avoid several complicated integrals appeared
in the course of the proof, by using a known estimate for the homogeneous wave equation due to
Klainerman (1984). We also modify the weight in such a way that the argument in the application
to the nonlinear problem becomes rather simple.
48 Tomonari Watanabe (Hiroshima Univ.) ♯ Global existence and decay estimates for quasilinear wave equations
with nonuniform dissipative term · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We study global existence and decay estimates for quasilinear wave equations with
nonuniform dissipative term. In the case of the nondissipative case, it is well known that no matter
how small the initial data, there do not exist time globally defined smooth solutions in general. But
we can prove the small data global existence by assuming the dissipation effective near the infinity,
even if equations behave the quasilinear wave equations on the bounded domain. Furthermore we
get the decay estimates with additional assumptions on initial data.
49 Itsuko Hashimoto
(Kanazawa Univ./Osaka City Univ.)
Heinrich Freistühler (Konstanz Univ.)
∗ Initial boundary value problem for scalar conservation law · · · · · · · · · · 10
Summary: We consider the initial boundary value problem with wide class of flux functions.
50 Naoki Tsuge (Gifu Univ.) ♯ The motion of the gas in a nozzle —Time global existence and invariant
regions— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We study the motion of isentropic gas in a nozzle. In the present talk, we consider
unsteady flow, which is governed by the compressible Euler equation, and prove the existence of
global solutions for the Cauchy problem. Although the flow is recently studied in some papers,
the monotonicity of the cross section area of the nozzle is assumed in these papers. Therefore,
we consider the general cross section area. When we prove the global existence, the most difficult
point is to obtain the bounded estimate for solutions. To overcome this, we employ a new invariant
region.