In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and init...In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.展开更多
In this paper,combining Riemann’s method with the fixed point theory effectively,we proved that the migration equation of the moisture in soil with nonlinear initial boundary value problem has unique classical solution.
In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages...In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.展开更多
By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomo...By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the as...This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H^s(0,1) for any s≥0 via the contraction mapping principle.展开更多
The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main in-gredient consists of estimating the change in moment...The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main in-gredient consists of estimating the change in momentum along characteristics of regular electric fields inside bounded spatial domains. As direct consequences, the propagation of the momentum moments and the existence of weak solution satisfying the balance of total energy are obtained.展开更多
This paper deals with some parabolic Monge-Ampère equation raised from mathematical finance: V_sV_(yy)+ryV_yV_(yy)-θV_y^2= 0(V_(yy) < 0). The existence and uniqueness of smooth solution to its initial-boundar...This paper deals with some parabolic Monge-Ampère equation raised from mathematical finance: V_sV_(yy)+ryV_yV_(yy)-θV_y^2= 0(V_(yy) < 0). The existence and uniqueness of smooth solution to its initial-boundary value problem with some requirement is obtained.展开更多
The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation a...The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.展开更多
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.
文摘In this paper,combining Riemann’s method with the fixed point theory effectively,we proved that the migration equation of the moisture in soil with nonlinear initial boundary value problem has unique classical solution.
基金Supported by the NNSF of China(10441002)Supported by NNSF of Henan Province(200510466011)
文摘In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
文摘In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.
基金Project supported by Specialized Research Fund for the Doctoral Program of Higher Education.
文摘By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.
基金supported by the Charles Phelps Taft Memorial Fund of the University of Cincinnatithe Chunhui program (State Education Ministry of China) under Grant No. 2007-1-61006
文摘This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H^s(0,1) for any s≥0 via the contraction mapping principle.
文摘The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main in-gredient consists of estimating the change in momentum along characteristics of regular electric fields inside bounded spatial domains. As direct consequences, the propagation of the momentum moments and the existence of weak solution satisfying the balance of total energy are obtained.
文摘This paper deals with some parabolic Monge-Ampère equation raised from mathematical finance: V_sV_(yy)+ryV_yV_(yy)-θV_y^2= 0(V_(yy) < 0). The existence and uniqueness of smooth solution to its initial-boundary value problem with some requirement is obtained.
基金supported by the National Natural Science Foundation of China (No. 10971135)the Program for New Century Excellent Talents of the Ministry of Education of China (No. NCET-07-0546)+2 种基金the University Young Teacher Sciences Foundation of Anhui Province (No. 2010SQRL145)Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. AE071202)the Quality Project Fund of Fuyang Teachers College (No. 2010JPKC07)
文摘The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.
