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We have established the existence and uniqueness of the local solution for (0.1)∂tu+∂x5u−u∂xu=0,00,u(x,0)=φ(x),00,\left\{\begin{array}{ll}{\partial }_{t}u+{\partial }_{x}^{5}u-u{\partial }_{x}u=0,& 0\lt x\lt 1,\hspace{1.0em}t\gt 0,\\ u\left(x,0)=\varphi \left(x),& 0\lt x\lt 1,\\ u\left(0,t)={h}_{1}\left(t),u\left(1,t)={h}_{2}\left(t),\hspace{0.33em}{\partial }_{x}u\left(1,t)={h}_{3}\left(t),& \\ {\partial }_{x}u\left(0,t)={h}_{4}\left(t),\hspace{0.33em}{\partial }_{x}^{2}u\left(1,t)={h}_{5}\left(t),& t\gt 0,\end{array}\right. in the study of Zhao and Zhang [Non-homogeneous boundary value problem of the fifth-order KdV equations posed on a bounded interval, J. Math. Anal. Appl. 470 (2019), 251–278]. A question arises naturally: Can the local solution be extended to a global one? This article will address this question. First, through a series of logical deductions, a global a priori estimate is established, and then the local solution is naturally extended to a global solution.

We have studied four 2D layered perovskites, including OA2PbI4 (RP phase), ODAPbI4 and BDAPbI4 (DJ phase), (GA)MAPbI4 (ACI phase), where OA is [(CmH2m+1)NH3](m = 8), ODA is [NH3(CH2)mNH3](m = 8), BDA is [NH3(CH2)mNH3](m = 4), and GA is [C(NH2)3]; RP, DJ, and ACI means Ruddlesden–Popper, Dion–Jacobson and alternating cations in the interlayer, respectively. The temperature dependence of absorption and photoluminescence (PL) spectra have been measured. From which the average phonon energy (electron-phonon interaction strength) is analyzed as around 34 (80), 47 (184), 50 (402), and 63 (758) with the unit of meV for OA2PbI4, ODAPbI4, BDAPbI4, and (GA)MAPbI4, respectively. Larger phonon energy indicates the involvement of more phonons in organic spacer layer, with the corresponding stronger electron-phonon interaction. Furthermore, ultrafast transient absorption spectroscopy proves that, when the excitation photon energy is serval hundred meV higher than bandgap, the excitons still are the major photoexcitations in OA2PbI4, but polarons are major one in ODAPbI4, BDAPbI4, and (GA)MAPbI4 films, no matter the excitonic transitions dominate the absorption at their band edges. This work proves the organic spacers can regulate electron–phonon interaction then optoelectronic properties in 2D perovskites profoundly, which have implications toward future rational design for relevant devices.

In this paper, we study the initial boundary problem of fifth-order Korteweg-de Vries equation with nonlinear boundary values. First, we establish a so-called sharp boundary trace regularity associated with the linearized fifth-order Korteweg-de Vries equation. Then, aided by the sharp boundary trace regularity, we verify that initial-boundary value problem of fifth-order Korteweg-de Vries equation with nonlinear boundary conditions is locally well-posed when initial and boundary values are properly chosen.

In order to study the influence of the structural parameters of the wound cylindrical honeycomb on the energy absorption characteristics, a finite element simulation model was first established. Then, using the controlled variable method, the influence of the side length of the corrugated sheet, the thickness of the corrugated sheet and the thickness of the flat sheet on the energy absorption characteristics of the honeycomb was systematically studied. Finally, the experiment is carried out and compared with the simulation results. The results show that as the side length of the corrugated sheet decreases, the thickness of the corrugated sheet and the thickness of the flat sheet increase, the average stress and volume ratio energy absorption of the honeycomb can be increased; reducing the side length of the corrugated sheet and increasing the thickness of the corrugated sheet can increase the mass specific energy absorption. The increase in the thickness of the flat sheet can reduce the mass specific energy absorption; the simulation model is accurate, and the results are in good agreement with the experimental results in the honeycomb deformation and energy absorption characteristics. This paper has done a more detailed study on the three parameters that affect the strength of the cylindrical honeycomb, which provides new ideas and theoretical support for the energy-absorbing components of the passive safety protection of rail transit.

CsPbBr3 nanoparticles with averaged size of 14 and 2.1 nm (named as 14 and 2 nmNP, respectively) are synthesized capping with the ligand of dodecylbenzene sulfonic acid (DBSA). Using ultrafast transient absorption spectroscopy, free carriers in 14 nmNP characterize with the slow thermalization (∼0.76 ps) and long carrier cooling time (∼1 ns), which could be due to the phonon bottleneck effect. On the other hand, excitons are major photoexcitations in 2 nmNP, presenting with fast thermalization (<100 fs) and short cooling time (∼50 ps); this effective energy dissipation in 2 nmNPs can be ascribed to the involvement of phonons in DBSA ligands. In both 14 and 2 nmNP, we find that the photoexcitation accumulation leads to an increase in the bandgap that can be understood by the Burstein–Moss band filling effect. These results provide insights into the intrinsic photophysics of CsPbBr3 perovskite nanocrystals with different confinement effects, supplying direct implications for optoelectronic applications. [ABSTRACT FROM AUTHOR]