The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied w...The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.展开更多
The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions a...The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.展开更多
The ultrafast dynamics of benzaldehyde upon 260, 271, 284, and 287 nm excitations have been studied by femtosecond pinup-probe time-of-flight mass spectrometry. A bi-exponential decay component model was applied to fi...The ultrafast dynamics of benzaldehyde upon 260, 271, 284, and 287 nm excitations have been studied by femtosecond pinup-probe time-of-flight mass spectrometry. A bi-exponential decay component model was applied to fit the transient profiles of benzaldehyde ions and fragment ions. At the S2 origin, the first decay of the component was attributed to the internal conversion to the high vibrational levels of S1 state. Lifetimes of the first component decreased with increasing vibrational energy, due to the influence of high density of the vibrational levels. The second decay was assigned to the vibrational relaxation of the S1 whose lifetime was about 600 fs. Upon 287 nm excitation, the first decay became ultra-short （-56 fs） which was taken for the intersystem cross from S1 to T2, while the second decay component was attributed to the vibrational relaxation. The pump-probe transient of fragment was also studied with the different probe intensity at 284 nm pump.展开更多
The dynamic compressive deformation of cellular titanium with regularly distributed cylindrical pores is investigated to evaluate the effect of shock attenuation and obtain the shock Hugoniot relationship of the mater...The dynamic compressive deformation of cellular titanium with regularly distributed cylindrical pores is investigated to evaluate the effect of shock attenuation and obtain the shock Hugoniot relationship of the material. Dynamic compression experiments are conducted at room temperature using a single-stage light gas gun. The Hugoniot relations between shock wave velocity and particle velocity for the cellular titanium samples with porosities 20% and 30% are obtained. The shock response of the regular cellular titanium shows a clear wave attenuation effect. Numerical simulations are also conducted to supplement the experimental study.Inelastic deformation is observed in the samples using optical micrographs, indicating that the deformation of pores contributes significantly to the shock wave attenuation of the cellular titanium material.展开更多
The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature...Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.展开更多
文摘The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.
基金The National Natural Science Foundation of China(No.10771032)
文摘The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.
基金V. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China （No.20633070 and No.20473090）.
文摘The ultrafast dynamics of benzaldehyde upon 260, 271, 284, and 287 nm excitations have been studied by femtosecond pinup-probe time-of-flight mass spectrometry. A bi-exponential decay component model was applied to fit the transient profiles of benzaldehyde ions and fragment ions. At the S2 origin, the first decay of the component was attributed to the internal conversion to the high vibrational levels of S1 state. Lifetimes of the first component decreased with increasing vibrational energy, due to the influence of high density of the vibrational levels. The second decay was assigned to the vibrational relaxation of the S1 whose lifetime was about 600 fs. Upon 287 nm excitation, the first decay became ultra-short （-56 fs） which was taken for the intersystem cross from S1 to T2, while the second decay component was attributed to the vibrational relaxation. The pump-probe transient of fragment was also studied with the different probe intensity at 284 nm pump.
基金supported by the National Natural Science Foundation of China(Grant Nos.11572049 and 11472036)
文摘The dynamic compressive deformation of cellular titanium with regularly distributed cylindrical pores is investigated to evaluate the effect of shock attenuation and obtain the shock Hugoniot relationship of the material. Dynamic compression experiments are conducted at room temperature using a single-stage light gas gun. The Hugoniot relations between shock wave velocity and particle velocity for the cellular titanium samples with porosities 20% and 30% are obtained. The shock response of the regular cellular titanium shows a clear wave attenuation effect. Numerical simulations are also conducted to supplement the experimental study.Inelastic deformation is observed in the samples using optical micrographs, indicating that the deformation of pores contributes significantly to the shock wave attenuation of the cellular titanium material.
基金supported by the National Science Foundation of China under Grant Nos.60225003,60334040,60221301,60774025,10831007,61104129,11171195the Excellent PhD Adviser Program of Beijing under Grant No.YB20098000101
文摘The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
基金supported by the National Natural Science Foundation of China (Nos.60225003,60821091,10831007,60774025)KJCX3-SYW-S01
文摘Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.
