We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical s...We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.展开更多
We consider the Cauchy problem of Euler equations with damping. Based on the Green function and energy estimates of solutions, we improve the pointwise estimates and obtainL 1 estimate of solutions.
In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorp...In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p(t) and q(t) are allowed to change sign on [t0,∞).
In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new ...In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.展开更多
The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and ...The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.展开更多
Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wav...Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.展开更多
In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is prop...In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.展开更多
Formulation of control objectives is a key issue in automatic control systems design. Although at first sight the desired goal (control objective) of a control system seems to be a trivial and obvious matter, for...Formulation of control objectives is a key issue in automatic control systems design. Although at first sight the desired goal (control objective) of a control system seems to be a trivial and obvious matter, for effectiveness of some high level robotic tasks, unusual exotic control objectives may be required. This paper presents a review of some exotic control objectives useful in robotics, such as velocity field control objective and range control objective. The paper also proposes a novel confinement control objective. The usefulness of these exotic control objectives may appear in safe robot-human interaction and self-protection of robots against collisions.展开更多
On highways,vehicles that swerve out of their lane due to sideslip can pose a serious threat to the safety of autonomous vehicles.To ensure their safety,predicting the sideslip trajectories of such vehicles is crucial...On highways,vehicles that swerve out of their lane due to sideslip can pose a serious threat to the safety of autonomous vehicles.To ensure their safety,predicting the sideslip trajectories of such vehicles is crucial.However,the scarcity of data on vehicle sideslip scenarios makes it challenging to apply data-driven methods for prediction.Hence,this study uses a physical model-based approach to predict vehicle sideslip trajectories.Nevertheless,the traditional physical model-based method relies on constant input assumption,making its long-term prediction accuracy poor.To address this challenge,this study presents the time-series analysis and interacting multiple model-based(IMM)sideslip trajectory prediction(TSIMMSTP)method,which encompasses time-series analysis and multi-physical model fusion,for the prediction of vehicle sideslip trajectories.Firstly,we use the proposed adaptive quadratic exponential smoothing method with damping(AQESD)in the time-series analysis module to predict the input state sequence required by kinematic models.Then,we employ an IMM approach to fuse the prediction results of various physical models.The implementation of these two methods allows us to significantly enhance the long-term predictive accuracy and reduce the uncertainty of sideslip trajectories.The proposed method is evaluated through numerical simulations in vehicle sideslip scenarios,and the results clearly demonstrate that it improves the long-term prediction accuracy and reduces the uncertainty compared to other model-based methods.展开更多
基金supported by the National Natural Science Foundation of China(11301172,11226170)China Postdoctoral Science Foundation funded project(2012M511640)Hunan Provincial Natural Science Foundation of China(13JJ4095)
文摘We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
基金the National Natural Science Foundation of China(1013105)
文摘We consider the Cauchy problem of Euler equations with damping. Based on the Green function and energy estimates of solutions, we improve the pointwise estimates and obtainL 1 estimate of solutions.
文摘In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p(t) and q(t) are allowed to change sign on [t0,∞).
文摘In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.
基金supported by the National Natural Science Foundation of China(No.11671369,No.12071443)Key Scientific Research Project of Colleges and Universities in Henan Province(No.20B110013).
文摘The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.
基金by the Subproject of Major Science and Technology Program of China(No.2017ZX07101001-01)the Fundamental Research Funds for the Central Universities(Nos.2018MS168 and 2020MS043).
文摘Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.
基金supported by Fundamental Research Funds for the Henan Provincial Colleges and Universities(No.20A110002).
文摘In this paper,the transient Navier-Stokes equations with damping are considered.Firstly,the semi-discrete scheme is discussed and optimal error estimates are derived.Secondly,a linearized backward Euler scheme is proposed.By the error split technique,the Stokes operator and the H^(-1)-norm estimate,unconditional optimal error estimates for the velocity in the norms L^(∞)(L^(2)) and L^(∞)(H^(1)),and the pressure in the norm L^(∞)(L^(2))are deduced.Finally,two numerical examples are provided to confirm the theoretical analysis.
文摘Formulation of control objectives is a key issue in automatic control systems design. Although at first sight the desired goal (control objective) of a control system seems to be a trivial and obvious matter, for effectiveness of some high level robotic tasks, unusual exotic control objectives may be required. This paper presents a review of some exotic control objectives useful in robotics, such as velocity field control objective and range control objective. The paper also proposes a novel confinement control objective. The usefulness of these exotic control objectives may appear in safe robot-human interaction and self-protection of robots against collisions.
基金supported by the National Natural Science Foundation of China(Grant No.51975310).
文摘On highways,vehicles that swerve out of their lane due to sideslip can pose a serious threat to the safety of autonomous vehicles.To ensure their safety,predicting the sideslip trajectories of such vehicles is crucial.However,the scarcity of data on vehicle sideslip scenarios makes it challenging to apply data-driven methods for prediction.Hence,this study uses a physical model-based approach to predict vehicle sideslip trajectories.Nevertheless,the traditional physical model-based method relies on constant input assumption,making its long-term prediction accuracy poor.To address this challenge,this study presents the time-series analysis and interacting multiple model-based(IMM)sideslip trajectory prediction(TSIMMSTP)method,which encompasses time-series analysis and multi-physical model fusion,for the prediction of vehicle sideslip trajectories.Firstly,we use the proposed adaptive quadratic exponential smoothing method with damping(AQESD)in the time-series analysis module to predict the input state sequence required by kinematic models.Then,we employ an IMM approach to fuse the prediction results of various physical models.The implementation of these two methods allows us to significantly enhance the long-term predictive accuracy and reduce the uncertainty of sideslip trajectories.The proposed method is evaluated through numerical simulations in vehicle sideslip scenarios,and the results clearly demonstrate that it improves the long-term prediction accuracy and reduces the uncertainty compared to other model-based methods.