Oscillation or nonoscillation property for semilinear wave equations

AbstractWe considerP±u=∂t2u−Δu±F(u)=0,where F(u)=au+f(u) with a⩾0 and f(0)=0. For the Cauchy problem of P+ if a>0, every nontrivial solution oscillates for any initial data. On the other hand for the Cauchy problem of P− if a⩾0, the solution does not change its sign for some initial data, namely it has nonoscillation property

Blow-Up of Positive Solutions to Wave Equations in High Space Dimensions

This paper is concerned with the Cauchy problem for the semilinear wave equation: u_{tt}-\Delta u=F(u) \ \mbox{in} \ R^n\times[0, \infty), where the space dimension $n \ge 2$, $F(u)=|u|^p$ or $F(u)=|u|^{p-1}u$ with $p>1$. Here, the Cauchy data are non-zero and non-compactly supported. Our results on the blow-up of positive radial solutions (not necessarily radial in low dimensions $n=2, 3$) generalize and extend the results of Takamura(1995) and Takamura, Uesaka and Wakasa(2011). The main technical difficulty in the paper lies in obtaining the lower bounds for the free solution when both initial position and initial velocity are non-identically zero in even space dimensions.Comment: 16page

Sharp blow-up for semilinear wave equations with non-compactly supported data

This paper corrects Asakura's observation on\ud semilinear wave equations with non-compactly supported data\ud by showing a sharp blow-up theorem for classical solutions.\ud We know that there is no global in time solution for any power nonlinearity\ud if the spatial decay of the initial data is weak,\ud in spite of finite propagation speed of the linear wave.\ud Our theorem clarifies the final criterion on such a phenomenon

Isotope production in proton-, deuteron-, and carbon-induced reactions on Nb 93 at 113 MeV/nucleon

Isotope-production cross sections for p-, d-, and C-induced spallation reactions on Nb93 at 113 MeV/nucleon were measured using the inverse-kinematics method employing secondary targets of CH2, CD2, and C. The measured cross sections for Mo90, Nb90, Y86,88 produced by p-induced reactions were found to be consistent with those measured by the conventional activation method. We performed benchmark tests of the reaction models INCL-4.6, JQMD, and JQMD-2.0 implemented in the Particle and Heavy Ion Transport code System (PHITS) and of the nuclear data libraries JENDL-4.0/HE, TENDL-2017, and ENDF/B-VIII.0. The model calculations also showed generally good agreement with the measured isotope-production cross sections for p-, d-, and C-induced reactions. It also turns out that, among the three nuclear data libraries, JENDL-4.0/HE provides the best agreement with the measured data for the p-induced reactions. We compared the present Nb93 data with the Zr93 data, that were measured previously by the same inverse kinematics method (Kawase et al., Prog. Theor. Exp. Phys. 2017, 093D03 (2017)2050-391110.1093/ptep/ptx110), with particular attention to the effect of neutron-shell closure on isotope production in p- and d-induced spallation reactions. The isotopic distributions of the measured production cross sections in the Zr93 data showed noticeable jumps at neutron number N=50 in the isotopic chains of ΔZ=0 and -1, whereas no such jump appeared in isotopic chain of ΔZ=0 in the Nb93 data. From INCL-4.6 + GEM calculations, we found that the jump formed in the evaporation process is smeared out by the intranuclear cascade component in Nb91 produced by the Nb93(p,p2n) and (d,d2n) reactions on Nb93. Moreover, for Nb93, the distribution of the element-production cross sections as a function of the change in proton number ΔZ is shifted to smaller ΔZ than for Zr93, because the excited Nb prefragments generated by the cascade process are more likely to emit protons than the excited Zr prefragments, due to the smaller proton-separation energies of the Nb isotopes

Coulomb breakup reactions of 93,94 Zr in inverse kinematics

Coulomb breakup reactions of 93,94 Zr have been studied in inverse kinematics at incident beam energies of about 200 MeV/nucleon in order to evaluate neutron capture reaction methods. The 93 Zr(n,γ) 94 Zr reaction is particularly important as a candidate nuclear transmutation reaction for the long-lived fission product 93 Zr in nuclear power plants. One- and two-neutron removal cross sections on Pb and C targets were measured to deduce the inclusive Coulomb breakup cross sections, 375 ± 29 (stat.) ± 30 (syst.) and 403 ± 26 (stat.) ± 31 (syst.) mb for 93 Zr and 94 Zr, respectively. The results are compared with estimates using the standard Lorentzian model and microscopic calculations. The results reveal a possible contribution of the pygmy dipole resonance or giant quadrupole resonance in the Coulomb breakup reactions of 94 Zr

Spallation reaction study for fission products in nuclear waste: Cross section measurements for 137

Spallation reactions for the long-lived fission products 137Cs, 90Sr and 107Pd have been studied for the purpose of nuclear waste transmutation. The cross sections on the proton- and deuteron-induced spallation were obtained in inverse kinematics at the RIKEN Radioactive Isotope Beam Factory. Both the target and energy dependences of cross sections have been investigated systematically. and the cross-section differences between the proton and deuteron are found to be larger for lighter fragments. The experimental data are compared with the SPACS semi-empirical parameterization and the PHITS calculations including both the intra-nuclear cascade and evaporation processes