In this paper, we consider a system of weakly coupled semilinear damped wave equations. We determine the critical exponent for any space dimensions. Our proof of the global existence of solutions for ...supercritical nonlinearities is based on a weighted energy method, whose multiplier is appropriately modified in the case where one of the exponent of the nonlinear term is less than the so called Fujita’s critical exponent. We also give estimates of the lifespan of solutions from above for subcritical nonlinearities.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercritical case for ...any space dimension. We also give estimates of the weighted energy of solutions and in a special case, we prove an almost optimal estimate. Moreover, in the subcritical case, we give an almost optimal estimate of the lifespan from both above and below.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We consider the Cauchy problem of the semilinear wave equation with a damping term
u
tt
-
Δ
u
+
c
(
t
,
x
)
u
t
=
|
u
|
p
,
(
t
,
x
)
∈
(
0
,
∞
)
×
R
N
,
u
(
0
,
x
)
=
ε
u
0
(
x
)
,
u
t
(
0
,
x
)
=
ε
...u
1
(
x
)
,
x
∈
R
N
,
where
p
>
1
and the coefficient of the damping term has the form
c
(
t
,
x
)
=
a
0
(
1
+
|
x
|
2
)
-
α
/
2
(
1
+
t
)
-
β
with some
a
0
>
0
,
α
<
0
,
β
∈
(
-
1
,
1
. In particular, we mainly consider the cases
α
<
0
,
β
=
0
or
α
<
0
,
β
=
1
,
which imply
α
+
β
<
1
, namely, the damping is spatially increasing and effective. Our aim is to prove that the critical exponent is given by
p
=
1
+
2
N
-
α
.
This shows that the critical exponent is the same as that of the corresponding parabolic equation
c
(
t
,
x
)
v
t
-
Δ
v
=
|
v
|
p
.
The global existence part is proved by a weighted energy estimates with an exponential-type weight function and a special case of the Caffarelli–Kohn–Nirenberg inequality. The blow-up part is proved by a test-function method introduced by Ikeda and Sobajima
15
. We also give an upper estimate of the lifespan.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We consider the Cauchy problem for the wave equation with overdamping and semilinear source terms:(P){utt−Δu+b(t)ut=N(u),(t,x)∈R+×RN(u,ut)(0,x)=(u0,u1)(x),x∈RN, with b(t)=b0(t+1)−β,b0>0,β<−1 and ...N(u)=|u|p−1u,p>1. Ikeda and Wakasugi 8 have recently showed that, when |N(u)|≤C|u|p for any p>1, there is a global-in-time solution to (P) for suitable small data, and that, when N(u)=±|u|p, the local-in-time solution blows up within a finite time for suitable large data. To show the blow-up result, their method seems to be not applicable to our semilinear term. Our aim is to show the blow-up of solutions for suitable large data, by the method much different from theirs.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
To investigate the applicability of the pulsed neutron source method using a pulsed spallation neutron source for an on-line subcriticality monitoring system of an accelerator-driven system, a ...subcritical experiment is conducted using the Kyoto University Critical Assembly in combination with the fixed-field alternating gradient accelerator. Reactivity values obtained from different traditional techniques, the area-ratio method and the α-fitting method, are discussed with respect to the applicability to on-line subcriticality monitoring. The results show that the area-ratio method robustly and accurately monitors subcriticality in shallow subcritical states with negative reactivity of up to a few dollars; however, this method faces problems with temporal fluctuations, spatial dispersion, and sensitivity to the proton-beam current with increasing depth of subcriticality. On the other hand, it is shown that the α-fitting method alleviates such problems in deep subcritical states. Moreover, a proposed fitting technique using the maximum-likelihood estimation method based on the Poisson distribution is robust enough to be applicable to on-line subcriticality monitoring for negative reactivity levels of up to roughly nine dollars.
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Nuclear Material Balance code version 4.0 (NMB4.0) has been developed through collaborative R&D between TokyoTech&JAEA. Conventional nuclear fuel cycle simulation codes mainly analyze actinides and ...are specialized for front-end mass balance analysis. However, quantitative back-end simulation has recently become necessary for considering R&D strategies and sustainable nuclear energy utilization. Therefore, NMB4.0 was developed to realize the integrated nuclear fuel cycle simulation from front- to back-end. There are three technical features in NMB4.0: 179 nuclides are tracked, more than any other code, throughout the nuclear fuel cycle; the Okamura explicit method is implemented, which contributes to reducing the numerical cost while maintaining the accuracy of depletion calculations on nuclides with a shorter half-life; and flexibility of back-end simulation is achieved. The main objective of this paper is to show the newly developed functions, made for integrated back-end simulation, and verify NMB4.0 through a benchmark study to show the computational performance.
In this paper, we consider the Cauchy problem for the wave equation with time dependent damping
b
(
t
)
u
t
and absorbed semilinear term
|
u
|
ρ
−
1
u
. Here,
b
(
t
)
=
b
0
(
1
+
t
)
−
β
with
−
1
<
β
...<
1
and
b
0
>
0
. Using the weighted energy method, we obtain the
L
1
and
L
2
decay rates of the solution, which coincide to those for self-similar solutions to the corresponding parabolic equation when
1
<
ρ
<
ρ
F
(
N
)
:
=
1
+
2
N
.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Reduction of burden caused by radioactive waste management is one of the most critical issues for the sustainable utilization of nuclear power. The Partitioning and Transmutation (P&T) technology ...provides the possibility to reduce the amount of the radiotoxic inventory of the high-level radioactive waste (HLW) dramatically and to extend the repository capacity. The accelerator-driven system (ADS) is regarded as a powerful tool to effectively transmute minor actinides (MAs) in the “double-strata” fuel cycle strategy. The ADS has a potential to flexibly manage MA in the transient phase from light water reactors (LWRs) to fast breeder reactors (FBRs), and can co-exist with FBR symbiotically and complementarily to enhance the reliability and the safety of the commercial FBR cycle. The concept of ADS in JAEA is a lead–bismuth eutectic (LBE) cooled, tank-type subcritical reactor with the power of 800
MWth driven by a 30
MW superconducting LINAC. By such an ADS, 250
kg of MA can be transmuted annually, which corresponds to the amount of MA produced in 10 units of LWR with 1
GWe. The design study was performed mainly for the subcritical reactor and the spallation target with a beam window. In Japan, Atomic Energy Commission (AEC) has implemented the check and review (C&R) on P&T technology from 2008 to 2009. In the C&R, the benefit of P&T technology, the current status of the R&D, and the way forward to promote it were discussed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Direct disposal concepts of mixed oxide spent fuel (MOXSF) consumed in light water reactors were investigated via heat transfer calculation. The temperature of the buffer material surrounding the ...waste is the most stringent limitation on the direct disposal of MOXSF. Therefore, the effects on the maximum temperature of the buffer material were examined by changing the occupied area, cooling term of MOXSF, disposal depth, and buffer material thickness referring to the direct disposal concepts of uranium spent fuel. Moreover, some possible disposal concepts for MOXSF were obtained based on the examination. The examination results showed that it is necessary to change the cooling term and disposal depth in addition to the change of the occupied area. The obtained disposal concepts with a combination of these changes needed the occupied area per unit waste of the MOXSF was three to five times that of uranium spent fuel.
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A new nuclear data library, JENDL/ImPACT-2018, was developed for an innovative study on the transmutation of long-lived fission products. Nuclear reaction cross-sections were newly evaluated for ...incident neutrons and protons up to 200 MeV for 163 nuclides focusing on long-lived nuclei such as
79
Se,
93
Zr,
107
Pd and
135
Cs, adopting some parts of JENDL-4.0. Our challenge was an evaluation of cross-sections for a number of unstable nuclei over a wide energy range where the experimental data were very scarce. We estimated cross-sections based on a nuclear model code CCONE by incorporating an advanced knowledge on the nuclear structure theory and a model-parameterization based on new experimental cross-sections measured by the inverse kinematics. Through comparisons with available experimental data on the stable isotopes, it is found that the present data give better agreements with them than those in the existing libraries. In a neutronics simulation by the PHITS code, we also found that the largest impact of the present library was seen on the estimated amount of isotope productions.
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