This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditi...This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.展开更多
Electroporation creates aqueous pathways by short high-voltage pulses resulting in a transient perme- abilization of stratum corneum and an increase in the transdermal delivery rate.However the aqueous pathways will r...Electroporation creates aqueous pathways by short high-voltage pulses resulting in a transient perme- abilization of stratum corneum and an increase in the transdermal delivery rate.However the aqueous pathways will reseal after pulsing,which leads to the rapid drop of transdermal flux.In the present study,the surfactants were added to the donor solution to hinder the shrinkage and resealing of the electropore,and to prolong the lifetime of the aqueous pathways with the consideration that the surfactants could reduce the surface energy of the electropore. These effects of surfactants were demonstrated by the dynamic electrical resistance of the skin and the fluorescent imaging of the local transport regions.Piroxicam(PIX)was transported percutaneously in the presence of surfac- tants in vitro.Owing to the longer lifetime of aqueous pathways,together with the promotion of PIX availability at the barrier exterior and the improvement in the partition of PIX into the aqueous pathways,the presence of surfac- tants led to a remarkable increase in the transdermal delivery rate during electroporation and a significant growth of the accumulative transdermal amount of PIX.展开更多
Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptima...Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.展开更多
The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent dampin...The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.展开更多
This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions wh...This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.展开更多
We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular cas...We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.展开更多
The Cauchy problem to the Oldroyd-B model is studied.In particular,it is shown that if the smooth solution （u,τ） to this system blows up at a finite time T～＊,then 0～T～＊u（t） L∞dt = ∞.Furthermore,the global ...The Cauchy problem to the Oldroyd-B model is studied.In particular,it is shown that if the smooth solution （u,τ） to this system blows up at a finite time T～＊,then 0～T～＊u（t） L∞dt = ∞.Furthermore,the global existence of smooth solution to this system is given with small initial data.展开更多
This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward gener...This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.展开更多
The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered re...The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.展开更多
基金Supported by the National Natural Science Foundation of China（10571024）
文摘This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.
基金Supported by the National Natural Science Foundation of China （No.20376038） and Tsinghua Basic Research Foundation （No.JCqn2005033）.
文摘Electroporation creates aqueous pathways by short high-voltage pulses resulting in a transient perme- abilization of stratum corneum and an increase in the transdermal delivery rate.However the aqueous pathways will reseal after pulsing,which leads to the rapid drop of transdermal flux.In the present study,the surfactants were added to the donor solution to hinder the shrinkage and resealing of the electropore,and to prolong the lifetime of the aqueous pathways with the consideration that the surfactants could reduce the surface energy of the electropore. These effects of surfactants were demonstrated by the dynamic electrical resistance of the skin and the fluorescent imaging of the local transport regions.Piroxicam(PIX)was transported percutaneously in the presence of surfac- tants in vitro.Owing to the longer lifetime of aqueous pathways,together with the promotion of PIX availability at the barrier exterior and the improvement in the partition of PIX into the aqueous pathways,the presence of surfac- tants led to a remarkable increase in the transdermal delivery rate during electroporation and a significant growth of the accumulative transdermal amount of PIX.
文摘Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.
基金Project supported by a grant of DFG (Deutsche Forschungsgemeinschaft) for the research project "Influence of time-dependent coefficients on semi-linear wave models" (No. RE 961/17-1)
文摘The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.
文摘This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.
基金supported by Australian Research Council’s Discovery Projects Funding Scheme(Grant No.DP120100895)
文摘We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.
文摘The Cauchy problem to the Oldroyd-B model is studied.In particular,it is shown that if the smooth solution （u,τ） to this system blows up at a finite time T～＊,then 0～T～＊u（t） L∞dt = ∞.Furthermore,the global existence of smooth solution to this system is given with small initial data.
基金supported by the National Science Foundation under Grant Nos. #DMS 0505472, 0806017,and#DMS 0604309
文摘This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.
基金the MST Grant #1999075107 and the Innovation funds of AMSS, CAS of China.
文摘The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.
